lemma-discovery-assistant

Name: lemma-discovery-assistant
Availability: InStock
Author: ArabelaTso

Analyze failed Isabelle/HOL and Coq proofs to propose auxiliary lemmas.

142|14|Updated Feb 14, 2026

Search Tags:#formal verification #theorem proving #proof assistant #coq #lemma generation #isabelle/hol

Ready to run

npx skills add https://github.com/ArabelaTso/Skills-4-SE --skill lemma-discovery-assistant

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: lemma-discovery-assistant
Source: https://github.com/ArabelaTso/Skills-4-SE/tree/main/skills/lemma-discovery-assistant
Command: npx skills add https://github.com/ArabelaTso/Skills-4-SE --skill lemma-discovery-assistant

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

This Skill helps users overcome proof failures in formal verification systems like Isabelle/HOL and Coq by identifying and suggesting necessary auxiliary lemmas.

Core Features & Use Cases

Proof State Analysis: Analyzes stuck proof states to pinpoint reasoning gaps.
Lemma Suggestion: Proposes precise lemma statements and proof strategies.
Use Case: When a complex inductive proof in Coq fails because a crucial intermediate property is missing, this Skill can analyze the failed subgoal and suggest a lemma that, once proven, allows the main proof to proceed.

Quick Start

Use the lemma discovery assistant to analyze the current proof state and suggest a lemma that will help complete the proof.

Frequently Asked Questions about lemma-discovery-assistant

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

FAQPage Schema

How do I find missing lemmas when my Coq proof is stuck?▼

To find missing lemmas in a stuck Coq proof, analyze the failed proof state to pinpoint reasoning gaps like weak induction hypotheses or insufficient rewrite rules, then propose auxiliary lemma statements that allow the proof to proceed.

What should I do when an inductive proof in Isabelle/HOL fails due to weak induction hypotheses?▼

When an inductive proof in Isabelle/HOL fails due to weak induction hypotheses, analyze the stuck proof state to identify the missing intermediate property and generate a generalization lemma with a tailored proof strategy to bridge the gap.

Can I get proof strategy suggestions alongside lemma statements for formal verification?▼

Yes, lemma generation for formal verification provides precise lemma statements, tailored proof strategies, and usage explanations for inductive, generalization, rewrite, and structural proof types to help complete complex proofs.

How does proof state analysis identify missing intermediate steps in theorem proving?▼

Proof state analysis identifies missing intermediate steps in theorem proving by examining stuck subgoals to detect reasoning gaps, insufficient rewrite rules, and weak induction hypotheses, then proposing the exact auxiliary lemmas needed to proceed.

Does the lemma discovery assistant work with both Coq and Isabelle/HOL?▼

Yes, the lemma discovery assistant works with both Coq and Isabelle/HOL by analyzing failed or stuck proofs in either system to propose auxiliary lemmas, addressing obstacles like missing intermediate steps and insufficient rewrite rules.