The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system – the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomolińska’s paper “A Comparative Study of Some Generalized Rough Approximations”, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.

中文翻译：

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一些广义粗糙近似的自动比较研究

本文包含了一些关于构建自动对等集的评论，这些对等集是对集合的一些广义粗糙近似的比较，其中经典不可区分关系被广义化为任意二元关系。我们的重点是通过Mizar系统（该软件和数据库可以表达和检查数学知识的逻辑正确性）来为此类算子翻译合理性假设。主要目的是从A.Gomolińska的论文“一些广义粗糙近似的比较研究”中获得定理4.1的形式证明（并经过机器检验），因此是现在的标题。我们还提供了有关如何使演示文稿更有效地重用Mizar验证程序的推理技术的讨论。