This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices in structuring proofs which make essential use of the tools of HOL Light and which differ in part from the standard strategies found in main textbooks covering the topic in an informal setting. Moreover, we propose a reflection on our own experience in using this specific theorem prover for this formalization task, with an analysis of pros and cons of reasoning within and about the formal system for GL we implemented in our code.

翻译：这项工作为HOL Light理论证明中G\'odel-L\'obclable problicity 逻辑(GL)提供了一个正式的模型完整性证明。 我们描述了我们制定的守则,并讨论了我们执行的一些细节,侧重于我们在结构证据方面的选择,这些选择对HOL Light工具至关重要,与在非正式环境中涉及该专题的主要教科书中的标准战略部分不同。此外,我们建议反思我们自己在利用这一具体理论证明完成这一正规化任务方面的经验,分析我们守则中执行的GL的正式系统内部的利弊和逻辑。