proof-assistant

# Proof Assistant Skill ## Purpose Assist in constructing formal correctness proofs for algorithms using standard proof techniques. ## Capabilities - Proof structure templates (induction, contradiction, etc.) - Step-by-step proof guidance - Termination argument generation - Proof review and validation - Identify proof gaps ## Target Processes - correctness-proof-testing - algorithm-implementation ## Proof Techniques ### Mathematical Induction - Base case identification - Inductive hypothesis formulation - Inductive step construction ### Proof by Contradiction - Assumption negation - Logical derivation - Contradiction identification ### Loop Invariant Proofs - Invariant specification - Three-part proof (init, maintenance, termination) ### Structural Induction - For recursive data structures - Base case (leaf/empty) - Inductive case (composite) ## Input Schema ```json { "type": "object", "properties": { "algorithm": { "type": "string" }, "code": { "type": "string" }, "proofType": { "type": "string", "enum": ["induction", "contradiction", "invariant", "structural"] }, "claim": { "type": "string" }, "partialProof": { "type": "string" } }, "required": ["algorithm", "claim"] } ``` ## Output Schema ```json { "type": "object", "properties": { "success": { "type": "boolean" }, "proof": { "type": "string" }, "structure": { "type": "array" }, "gaps": { "type": "array" }, "suggestions": { "type": "array" }...