arXiv:2602.02561v3 Announce Type: replace-cross Abstract: While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits Lean's usability as an everyday tool for mathematicians like \LaTeX{} or Maple. To address this, we introduce MathlibLemma, a modular LLM-based pipeline for automated folklore-lemma mining: the discovery, formalization, and proving of reusable intermediate facts that mathematicians often take for grant
The increasing maturity of large language models (LLMs) and the growing ecosystem around formal proof assistants like Lean and Mathlib make automated lemma generation a timely and critical development.
This development significantly enhances the practical utility of formal mathematics by automating a bottleneck in theorem proving, making these tools more accessible and efficient for mathematicians.
The ability to automatically discover, formalize, and prove 'folklore lemmas' fundamentally changes the workflow for formal mathematics, shifting from manual expert input to LLM-assisted generation.
- · Formal mathematics community
- · AI research in reasoning
- · Software verification
- · Academic institutions
- · Researchers reliant solely on manual proof generation
Increased pace of formal theorem proving and expansion of formalised mathematical knowledge bases.
Broader adoption of formal methods in areas like software engineering and cryptographic proof due to reduced entry barriers.
The development of new mathematical theories that are highly dependent on extensive formal verification from their inception.
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Read at arXiv cs.LG