Lax Lean Archive

An Introduction to Lax

lax-242665·formalized by Édouard Bonnet @EdouardBonnet · Jan Dreier · Clemens Kuske·registered·created ·GitHub @3f1a055·Lean v4.33.0 epoch · mathlib db584cd6d46c

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    Abstract

    An introduction to Lax, written as a Lax submission. Lax is an archive that links natural-language mathematics with Lean formalizations: submissions consist of concepts (a statement in prose paired with a faithful Lean encoding), proofs (Lean code discharging a concept's claim), and optionally the paper itself, annotated with markers that tie its passages to the concepts and proofs. This document walks through all three using the prime numbers as a running example: the definition of a prime, Euclid's theorem that there are infinitely many, the lemma on prime divisors it rests on, and the twin prime conjecture as a concept without a proof.

    View annotated paper

    5 pages · 10 marked passages

    Concepts

    Concept map
    4 concepts; 1 descendant hidden
    100%
    Proven claimOpen claimDefinitionThis submissionOther submissionA → B: B builds on A

    Proofs

    Proof networkview on GitHub

    100%
    assumptions conclusionProven claimOpen claimClaim from this submissionProof — open large view for details
    Proof list

    Lean sources for these proofs: proofs/ on GitHub

    Proof code is not displayed; the archive records each proof's checked relationship between claims.

    Related submissions

    Submission map

    100%
    This submissionOther submissionA → B: B's concepts build on AA → B: only B's proofs build on A

    Cite this

    This is only the formalizers. The authors of the formalized results may be different (see References).

    @misc{lax-242665,
  author = {Édouard Bonnet and Jan Dreier and Clemens Kuske},
  title = {An Introduction to Lax},
  year = {2026},
  howpublished = {Lax Archive, lax-242665},
  url = {https://laxarchive.org/lax-242665/},
}

    References

    1. Radosław Piórkowski. ReflowTeX: reflowable web rendering of sources. https://github.com/radek-p/reflowtex, 2026.
    2. The mathlib Community. The Lean Mathematical Library. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020) 367–381, 2020. doi:10.1145/3372885.3373824

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