lean-counterexample

Identify counterexamples in Lean conjectures using plausible and decide tactics.

Updated Mar 16, 2026
One-click install
npx skills add https://github.com/my04337/shapez2-in-lean --skill lean-counterexample
Or copy as Structured Prompt for Agent
Please help me install this Agent Skill.
Skill: lean-counterexample
Source: https://github.com/my04337/shapez2-in-lean/tree/main/.github/skills/lean-counterexample
Command: npx skills add https://github.com/my04337/shapez2-in-lean --skill lean-counterexample

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Systematically identify counterexamples to conjectures in Lean before attempting formal proofs, guiding early investment decisions and reducing wasted effort on false statements.

Core Features & Use Cases

  • Systematic counterexample search for Lean theorem candidates and lemmas.
  • Guided proof planning by validating conjectures at multiple levels and providing early risk assessment.
  • Workflow integration with Lean REPL, Scratch tests, and rapid evaluation using plausible and decide tactics.

Quick Start

Run the counterexample checker on your Lean file to quickly assess whether a conjecture holds before proving.

Frequently Asked Questions about lean-counterexample

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

FAQPage Schema
How do I find counterexamples to a Lean conjecture before attempting a formal proof?

To find counterexamples in Lean before formal proofs, run the systematic counterexample checker on your Lean file. This validates conjectures early using plausible and decide tactics, reducing wasted proof effort on false statements.

What is the best way to validate Lean lemmas and avoid investing in false conjectures?

The best way to validate Lean lemmas is systematic counterexample search before proof planning. This provides early risk assessment for theorem development by testing conjectures with rapid evaluation, avoiding wasted effort on false statements.

Does the counterexample checker work with Lean REPL and plausible tactics?

Yes, the counterexample checker integrates directly with Lean REPL, Scratch tests, and rapid evaluation using plausible and decide tactics. This workflow integration supports finite-type reasoning to test theorem candidates effectively.

When do I need to check for counterexamples in Lean theorem development?

You need to check for counterexamples in Lean theorem development before constructing formal proofs. Identifying counterexamples early guides proof planning and prevents investing effort in false conjectures during lemma validation.

Can I use decide tactics for finite-type reasoning to test Lean theorem candidates?

Yes, you can use decide and plausible tactics for finite-type reasoning to test Lean theorem candidates. The counterexample checker supports rapid evaluation through REPL-based testing to validate conjectures before formal proof construction.

What are the limitations of systematic counterexample search for Lean proofs?

The systematic counterexample search for Lean proofs is limited to finite-type reasoning and quick evaluation. It focuses on early risk assessment for plausible and decide tactics, and may not cover complex infinite-type theorem domains.