Abstract
The field of p-adic numbers p and the ring of p-adic integers p are essential constructions of modern number theory. Hensels lemma, described by Gouva as the most important algebraic property of the p-adic numbers, shows the existence of roots of polynomials over p provided an initial seed point. The theorem can be proved for the p-adics with significantly weaker hypotheses than for general rings. We construct p and p in the Lean proof assistant, with various associated algebraic properties, and formally prove a strong form of Hensels lemma. The proof lies at the intersection of algebraic and analytic reasoning and demonstrates how the Lean mathematical library handles such a heterogeneous topic.
Original language | English |
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Title of host publication | CPP 2019 - Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, Co-located with POPL 2019 |
Editors | Assia Mahboubi |
Publisher | Association for Computing Machinery, Inc |
Pages | 15-26 |
Number of pages | 12 |
ISBN (Electronic) | 9781450362221 |
DOIs | |
Publication status | Published - 14 Jan 2019 |
Event | 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2019 - Cascais, Portugal Duration: 14 Jan 2019 → 15 Jan 2019 |
Conference
Conference | 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2019 |
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Country | Portugal |
City | Cascais |
Period | 14/01/19 → 15/01/19 |
Keywords
- formal proof
- Hensel's lemma
- Lean
- p-adic