Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and Computation", to thousands of undergraduate students. In our companion paper, we presented our calculational proof format, gave an overview of the calculational proof checker (CPC) tool that we developed to help users write and validate proofs, described some of the technical and implementation details of CPC and provided several publicly available proofs written using our format. In this paper, we dive deeper into the implementation details of CPC, highlighting how proof validation works, which helps us argue that our proof checking process is sound.

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