Generate Lean 4 proofs for categorical laws and verification reports.
npx skills add https://github.com/BellaBe/lean-os --skill verify-laws
Please help me install this Agent Skill. Skill: verify-laws Source: https://github.com/BellaBe/lean-os/tree/main/.claude/skills/engineering-verify-laws Command: npx skills add https://github.com/BellaBe/lean-os --skill verify-laws
This Skill automates the generation and verification of proofs for categorical laws, producing Lean 4 proofs and a structured verification report.
Example: "Generate Lean proofs for left_id and assoc in LeanOS.Category using artifacts/v1/build/category.yaml."
High-intent search queries and answers about installing and using this skill.
Lean 4 proofs for categorical laws are generated by translating category, monad, functor, and transformation definitions into Lean syntax, then automatically enumerating and proving associated laws. The Skill converts your artifact definitions, states theorems, attempts proof strategies (reflexivity, simplification, or placeholders), runs lake build, and outputs verified proofs to artifacts/v{N}/verify/proofs with a laws-report.yaml summary.
Formal verification in Lean requires structured artifact definitions specifying categories, monads, functors, and natural transformations with their types and morphisms. The Skill accepts artifacts/v{N}/build/category.yaml format containing categorical structure definitions, which it translates into Lean definitions to generate and verify proofs.
Yes. Formal verification handles multiple categorical structures in a single workflow—monad laws, functor laws, and natural transformations can all be verified together. The Skill enumerates all applicable laws across your definitions and generates proofs for each, consolidating results in the laws-report.yaml.
The verification report (laws-report.yaml) documents proof status for each categorical law, including which proofs succeeded via reflexivity or simplification, which remain unsolved (sorry), and summary statistics. It provides structured output for auditing proof completeness and identifying laws requiring manual intervention.
Category theory translates to Lean through type-based representation of categories, morphisms, and lawful structures. The Skill maps categorical definitions to Lean types and morphism compositions, then applies proof tactics (reflexivity for definitional equality, simplification for derived laws) to automatically discharge or scaffold proofs.
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