We have formalised Szemer\'edi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant Isabelle/HOL. For the latter formalisation, we used the former to first show the Triangle Counting Lemma and the Triangle Removal Lemma: themselves important technical results. Here, in addition to showcasing the main formalised statements and definitions, we focus on sensitive points in the proofs, describing how we overcame the difficulties that we encountered.
翻译:我们正式化了Szemer\'edi的定时Lemma和Roth的关于自然进化的理论,这是利用校对助理Isabelle/HOL在极端图学理论和添加剂组合法中的两个主要结果。对于后者的正规化,我们利用前者首先展示了Lemma三角计数和Lemma三角清除:它们本身就是重要的技术成果。这里除了展示主要的正式声明和定义外,我们还侧重于证据中的敏感点,说明我们如何克服我们遇到的困难。