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Using a Sledgehammer to Crack Some Nuts

机译：用大锤破解一些坚果

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摘要

As mathematicians, we are generally used to proving results 'from the bottom up' so to speak. In other words, in order to prove what might be regarded as a relatively difficult theorem, we start with slightly more elementary results (often called lemmas) and gradually build up layer upon layer of complexity as we head towards our goal. I thought it might be fun to commit a form of mathematical heresy, and to try to do things the other way round; hence the title of this article. When doing something such as this there is of course always the potential for circular arguments to arise. These occur when theorem X is used to prove theorem Y that was itself assumed in order to prove theorem X! We note here that it is not necessary to assume either of the 'nuts' considered in this article in order to prove the 'sledgehammer'.
机译：作为数学家，我们通常习惯于“自下而上”证明结果。换句话说，为了证明什么可能被认为是一个相对困难的定理，我们从基本结果（通常称为引理）开始，然后逐步朝着目标前进，逐步形成复杂性。我认为提交数学异端形式并尝试以另一种方式做事可能会很有趣。因此，本文的标题。当做这样的事情时，当然总会出现循环争论的可能性。当定理X用于证明定理Y时，这些定理就会发生，而定理Y本身就是为了证明定理X！我们在这里注意到，不必为了证明“大锤”而假设本文考虑的两个“坚果”。

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