Reformalization of the Jordan Curve Theorem

Simon Guilloud; Sankalp Gambhir; Samuel Chassot

Reformalization of the Jordan Curve Theorem

Artificial Intelligence 2026-07-02 v1

Authors: Simon Guilloud , Sankalp Gambhir , Samuel Chassot

Abstract

We present a case study in reformalization, a variant of autoformalization in which the input proof is not natural language but a formal development in a different proof assistant. Concretely, we report three reformalizations of the Jordan Curve Theorem: from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. We analyse the results and identify pipeline design choices that matter for practical reformalization tasks.

Keywords

reformalization autoformalization Jordan curve theorem proof assistant Mizar Lean HOL Light Agda

Cite

@article{arxiv.2607.01734,
  title  = {Reformalization of the Jordan Curve Theorem},
  author = {Simon Guilloud and Sankalp Gambhir and Samuel Chassot},
  journal= {arXiv preprint arXiv:2607.01734},
  year   = {2026}
}