What question did this study set out to answer?

The aim is to construct a formal proof from ZFC set-theory axioms to a verified Turing machine program.

June 20, 2026Open Access

Book-Guided, LLM-Detailed, Kernel-Verified: Formal Proof Construction from ZFC Axioms to Program Correctness

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CYChenkan Yu

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Implication

Formal proof development demonstrates verified program correctness using axioms and a proof kernel, suggesting new directions for formal verification.

Key Points

The aim is to construct a formal proof from ZFC set-theory axioms to a verified Turing machine program.
Developed proofs guided by a textbook while using a Large Language Model (LLM) for detailed elaboration.
All 246 theorems checked using a 622-line custom C proof kernel.
Implemented a pure-functional proof language with persistent caching.
Successfully proved correctness of a 5-state unary addition program.
Achieved soundness of the proof independent of the LLM's input.
Established clear separation between kernel and userspace in the proof environment.

Cite This Study

Chenkan Yu (2026) studied this question.

synapsesocial.com/papers/6a363274db0793dc1a539032 https://doi.org/10.5281/zenodo.20746796

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Implication

Formal proof development demonstrates verified program correctness using axioms and a proof kernel, suggesting new directions for formal verification.

Book-Guided, LLM-Detailed, Kernel-Verified: Formal Proof Construction from ZFC Axioms to Program Correctness

Discussion

Member takes

Implication

Key Points

Cite This Study

Book-Guided, LLM-Detailed, Kernel-Verified: Formal Proof Construction from ZFC Axioms to Program Correctness

Discussion

Member takes

Implication

Key Points

Cite This Study

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