We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l (2002), and Han\v{c}l and Rucki (2005). Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization and discuss what this reveals about the use and potential of Isabelle/HOL in formalizing modern mathematical research, particularly in these parts of number theory and analysis.
翻译：我们从证明助理Isabelle/HOL中概述了我们从三份不同研究论文(Erd\H{o}s和Straus(1974年)、Han\v{c}l(2002年)、Han\v{c}l和Rucki(2005年))中,对证明助理Isabelle/HOL关于某些非理性和无限系列标准的正规化。我们在Isabelle/HOL的正式化可在正式证据档案中找到。这里我们描述了正规化的选定方面,并讨论了这揭示了Isabelle/HOL在使现代数学研究正规化,特别是在数字理论和分析的这些部分中,对现代数学研究的利用和潜力。
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