Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom's BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also {\eta}, delay and weak bisimilarity.

中文翻译：

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分支双相似性的最新技术

自从在过程中引入行为等价以来，人们一直在寻找伴随这些等价的有效证明技术。强双相似性和弱双相似性都伴随着一系列最新技术：它们的证明方法的增强。对于分支双相似性，这些结果尚未确定。我们通过结合 Bloom 的 BB 酷格式的 up to union、up to expand 和 up to context 三种技术，证明了一种强大的证明技术对于分支双相似性是合理的。然后，我们提出了在抽象代数设置中投射 up to context 技术的正确性证明的初步建议，涵盖分支以及 {\eta}、延迟和弱双相似性。