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pz: Skill for Claude Code

.claude/skills/lean/SKILL.md

lean is a skill for Claude Code from joelreymont/pz. It costs 32 tokens per session (598 once invoked), scanned C, original, MIT.

A build-and-check workflow for Lean 4 formal proofs. Lean is a programming language and proof checker that verifies whether stated mathematical claims follow from their definitions and assumptions.

In plain words
What is it for?
Use it to build and type-check proofs, add a new proof module, update dependencies, or repair the Lean project when its build files or cache need attention.
Why use it?
It catches errors in proof files and confirms that the formal verification project still builds after changes. It also describes how to recover a broken dependency cache and add new proofs.

Skill for Claude Code

Written for Claude Code: user-invocable in frontmatter.

This is joelreymont/pz's own configuration. It tells Claude Code how to work on pz itself, so it is not a mod to install elsewhere. Copy it as a starting point and replace the rules that are about this project. Everything pz configures →

not rated 100repo +1 7mo ago C scan 32 tokens original MIT
View source ↗ joelreymont/pz
Reuse

Borrowing it

Nothing to install: this file belongs to joelreymont/pz. Take a copy, put it at the same path in your own repository, and replace the rules that are about this project with yours.

Copy the file
curl -O https://raw.githubusercontent.com/joelreymont/pz/main/.claude/skills/lean/SKILL.md
Clone the repo
git clone --depth 1 https://github.com/joelreymont/pz

Made for: Claude Code.

Wrote this? Show the measurements

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Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

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Per session 32 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 598 The whole file, excluding the scripts and references it only reads on demand.
Security scan C 1 finding. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00032 $0.00598
Opus 5.5 $0.00013 $0.00239
Sonnet 5.5 $0.00006 $0.00120
Haiku 4.5 $0.00003 $0.00060

Measured 2mo ago against content hash a4b70ebe1f72, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

Grade C, and why

lean scanned grade C with 1 finding against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 2mo ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Recursive force deletehighDestructive command

rm -rf with a variable or a broad path is one typo away from removing the wrong tree.

If `.lake/` is corrupt: `rm -rf .lake && lake update && lake build`.
.claude/skills/lean/SKILL.md · 71 lines

How it starts

The opening of the file, as written. The whole thing — 71 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Lean 4 Proofs

Build and type-check the formal verification proofs in lean/.

Toolchain

  • elan: ~/.elan/bin/
  • lean/lake/leanc: all via elan
  • Project: lean/ in pz root, initialized with lake init pz-proofs math

Build

cd lean && ~/.elan/bin/lake build

First build downloads mathlib (~10 min). Subsequent builds are incremental (~seconds).

If .lake/ is corrupt: rm -rf .lake && lake update && lake build. After adding a dependency to lakefile.toml: lake update before lake build.

Project Structure

lean/
  lakefile.toml          # project config, mathlib dependency
  lean-toolchain         # pinned lean version
  PzProofs.lean          # root module (imports all proof files)
  PzProofs/
    Basic.lean           # auto-generated stub
    Mask.lean            # Proof 1: tool mask sanitization
    Approval.lean        # Proof 4: approval flow (future)
    Policy.lean          # Proof 2: signed policy (future)
    Ownership.lean       # Proof 3: file ownership (future)
    Crypto.lean          # abstract signature scheme (future)

Adding a Proof

  1. Create lean/PzProofs/Name.lean
  2. Add import PzProofs.Name to lean/PzProofs.lean
  3. cd lean && ~/.elan/bin/lake build
  4. If it type-checks, the proof is valid

Key Tactics

  • bv_decide: automatic bitvector reasoning via SAT. Handles all mask proofs.
  • omega: linear arithmetic over naturals/integers
  • simp: simplification with lemma database
  • intro/exact/have: manual proof steps
  • by decide: decidable propositions (finite enums, bool)

BitVec for Mask Proofs

Zig u16 maps to Lean BitVec 16. Operations:

  • &&& = bitwise AND, ||| = bitwise OR, ~~~ = complement
  • <<< = shift left, ≤ = unsigned less-or-equal
  • .getLsbD i = get bit at position i

bv_decide solves all fixed-width bitvector properties exhaustively.

Proof Plan

See docs/LEAN-PROOF.md for the full verification plan with 4 proofs, acceptance criteria, and dependencies.

Read the full file on GitHub · 71 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 2mo ago First seen · 71 lines · 32 tokens per session scan C a4b70ebe1f72

Subscribe to this mod's changes

lean is a skill published in the GitHub repository joelreymont/pz (100 stars, last pushed 7mo ago), licensed MIT. It adds 32 tokens to every session and 598 once invoked, about $0.0001 per session on Opus 5.5. A static security scan graded it C with 1 finding (recursive force delete). No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

Scientific
Related

lean compared with skills from other repositories

lean next to 6 skills from other repositories
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