We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion in mathlib, which is a community-driven effort to build a unified mathematics library for Lean. One goal of the mathlib project is to contain all of the topics of a complete undergraduate mathematics education. We provide three presentations of the main theorem statement: in terms of indexed families of finite sets, of relations on types, and of matchings in bipartite graphs. We also formalize a version of K\H{o}nig's lemma (in terms of inverse limits) to boost the theorem to the case of countably infinite index sets. We give a description of the design of the recent mathlib library for simple graphs, and we also give a necessary and sufficient condition for a simple graph to carry a function.

中文翻译：

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在精益中形式化霍尔的婚姻定理

我们将Lean定理证明者中的Hall婚姻定理形式化，以包含在mathlib中，这是社区推动的工作，旨在为Lean建立统一的数学库。mathlib项目的目标之一是包含完整的大学数学教育的所有主题。我们提供了三个主要定理陈述的表示形式：关于有限集的索引族，关于类型的关系以及对偶图的匹配。我们还形式化了K \ H {o} nig引理的一个形式（根据逆极限），以将定理推导到可数无限索引集的情况下。我们给出了用于简单图的最新mathlib库的设计描述，并且还给出了简单图带有函数的必要和充分条件。