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Enable automation for disjunction elimination and implication reasoning

Develop automated proof-tree construction in Coq for the veracity logic that supports reasoning about disjunction (or) elimination and implication rules, overcoming current limitations of the automation framework.

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Background

The mechanization currently supports only a simplified subset of the logic’s rules. The authors note that the existing automation works without evidence-dependent types, which restricts the capability to reason about certain rules.

They explicitly state that automated reasoning for or-elimination and implications is not yet achievable within their present framework, highlighting a concrete technical gap to be addressed.

References

In particular, reasoning about `or' elimination and implications in a way which supports automation is not yet possible.

— A Logic for Veracity: Development and Implementation (2407.16117 - Britten et al., 23 Jul 2024) in Section “Future Work”