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.

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., 2024) in Section “Future Work”