Individual skill

lemma-discovery-assistant

Analyze failed or stuck proofs and propose auxiliary lemmas to help complete the proof in Isabelle/HOL or Coq. Use when encountering proof failures, stuck proof states, unprovable subgoals, or when needing to strengthen induction hypotheses. Identifies missing lemmas, suggests proof strategies, and generates helper lemmas with appropriate statements and proof sketches. Supports inductive proofs, case analysis, rewriting, and complex proof obligations.

skills/lemma-discovery-assistant/SKILL.md

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Repository stars (not skill ratings): 260
Repository last updated: Aug 21, 2026
License: Apache-2.0

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SKILL.mdcore · 10,955 bytes
references/coq_lemmas.mddoc · 9,950 bytes
references/isabelle_lemmas.mddoc · 9,317 bytes
references/proof_patterns.mddoc · 10,418 bytes

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# Lemma Discovery Assistant

Analyze stuck or failed proofs and propose auxiliary lemmas that can help complete the proof.

## Overview

When proofs fail or get stuck, the issue is often a missing auxiliary lemma. This skill helps identify what lemmas are needed by:

1. Analyzing the current proof state and goal
2. Identifying gaps in reasoning
3. Proposing auxiliary lemmas with precise statements
4. Suggesting proof strategies for the lemmas
5. Explaining how the lemmas help the main proof