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arXiv · 2404.11638

Chain Bounding, the leanest proof of Zorn's lemma, and an illustration of computerized proof formalization

Guillermo L. Incatasciato·Pedro Sánchez Terraf
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Abstract

We present an exposition of the *Chain Bounding Lemma*, which is a common generalization of both Zorn's Lemma and the Bourbaki-Witt fixed point theorem. The proofs of these results through the use of Chain Bounding are amongst the simplest ones that we are aware of. As a by-product, we show that for every poset $P$ and function $f$ from the powerset of $P$ into $P$, there exists a maximal well-ordered chain whose family of initial segments is appropriately closed under $f$. We also provide an introduction to the process of "computer formalization" of mathematical proofs by using *proofs assistants*. As an illustration, we verify our main results with the Lean proof assistant.

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Guillermo L. Incatasciato, Pedro Sánchez Terraf. 2024-10-30. Chain Bounding, the leanest proof of Zorn's lemma, and an illustration of computerized proof formalization. https://arxiv.org/abs/2404.11638

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