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DOI: 10.4230/LIPIcs.ITP.2022.23
URN: urn:nbn:de:0030-drops-167326
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16732/
Kudryashov, Yury
Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean
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Abstract
I formalize a version of the divergence theorem for a function on a rectangular box that does not assume regularity of individual partial derivatives, only Fréchet differentiability of the vector field and integrability of its divergence. Then I use this theorem to prove the Cauchy-Goursat theorem (for some simple domains) and bootstrap complex analysis in the Lean mathematical library. The main tool is the GP-integral, a version of the Henstock-Kurzweil integral introduced by J. Mawhin in 1981. The divergence theorem for this integral does not require integrability of the divergence.
BibTeX - Entry
@InProceedings{kudryashov:LIPIcs.ITP.2022.23,
author = {Kudryashov, Yury},
title = {{Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean}},
booktitle = {13th International Conference on Interactive Theorem Proving (ITP 2022)},
pages = {23:1--23:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-252-5},
ISSN = {1868-8969},
year = {2022},
volume = {237},
editor = {Andronick, June and de Moura, Leonardo},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16732},
URN = {urn:nbn:de:0030-drops-167326},
doi = {10.4230/LIPIcs.ITP.2022.23},
annote = {Keywords: divergence theorem, Green’s theorem, Gauge integral, Cauchy integral formula, Cauchy-Goursat theorem, complex analysis}
}
| Keywords: | divergence theorem, Green’s theorem, Gauge integral, Cauchy integral formula, Cauchy-Goursat theorem, complex analysis | |
| Seminar: | 13th International Conference on Interactive Theorem Proving (ITP 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 03.08.2022 | |
| Supplementary Material: | InteractiveResource (Documentation Website): http://div-thm.urkud.name/ |
