Can I use this for non-mathematical coding tasks?

While primarily designed for mathematical theorem proving, it can be applied to any domain requiring formal logic verification and state-chain documentation within the Lean 4 framework.

What is the GF(3) triad structure used in this skill?

The triad structure is a balanced verification system consisting of three agents: a Generator (+1), a Coordinator (0), and a Validator (-1). Their total 'trit' sum must always equal zero to ensure the soundness of the proof transition.

Does this skill work with Lean 3?

No, this skill is specifically designed for Lean 4, utilizing its modern syntax and tactic ecosystem for generating formal proof states.

What is the output of a proof walk?

The skill emits four distinct components: a formal Lean 4 statement, a brief informal proof, a numbered detailed informal proof, and the complete chain of proof states showing the evolution of the goal.

Lean Proof Walk

Name: Lean Proof Walk
Author: plurigrid

byplurigrid

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Security & Testing

Generates formal Lean 4 proof state chains using a GF(3)-balanced triad agent system for rigorous mathematical verification.

Lean Proof Walk is a specialized formal methods skill that leverages a GF(3)-balanced random walk to traverse complex proof spaces within the Lean 4 environment. By employing a unique triad architecture—consisting of a Generator, Coordinator, and Validator—it ensures logical soundness and GF(3) conservation across every state transition. This skill is particularly useful for developers and mathematicians who need to bridge the gap between informal reasoning and formal machine-checked proofs, providing granular state-by-state chains, seed-based reproducibility, and both informal and formal output structures for complete theorem verification.

Key Features

018 GitHub stars

02Comprehensive Proof Output: Generates formal statements, informal summaries, and detailed step-by-step state-context chains.

03Reproducible Seed System: Allows users to provide specific seeds for deterministic traversal of the proof space.

04GF(3) Conservation Logic: Uses a balanced mathematical invariant system to maintain the integrity of state transitions.

05Lean 4 Tactic Integration: Supports standard tactics including induction, cases, ring, and omega for complex proof navigation.

06Parallel Triad Verification: Employs three synchronized agents (Generator, Coordinator, Validator) to ensure proof soundness.

Use Cases

01Automating the construction of formal proofs for mathematical propositions in Lean 4.

02Verifying complex software invariants and logical properties using machine-checked formal methods.

03Developing educational documentation that explains formal logic through interleaved state-chain visualizations.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi lean-proof-walk

For use in Claude.ai and ChatGPT

Download Skill