proof-theory

Solve proof theory problems using direct proof, contradiction, cases, and induction.

8|1|Updated Jan 4, 2026

Search Tags:#formal verification #theorem proving #mathematical logic #induction #proof theory #Z3 solver

Ready to run

npx skills add https://github.com/scooter-lacroix/Maestro --skill proof-theory

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: proof-theory
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/mathematical-logic/proof-theory
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill proof-theory

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires z3-solver, math_scratchpad, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill assists in solving problems related to proof theory within mathematical logic, offering strategies and tools for constructing and verifying proofs.

Core Features & Use Cases

Proof Strategy Selection: Guides users through choosing appropriate proof methods like direct proof, contradiction, cases, or induction.
Automated Proof Assistance: Leverages tools like Z3 solver for induction principles and soundness checks.
Use Case: When faced with a complex theorem in mathematical logic, this Skill can help you select the most effective proof strategy and even assist in verifying specific steps using automated solvers.

Quick Start

Use the proof-theory skill to verify the soundness of a theorem.

Frequently Asked Questions about proof-theory

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I verify the soundness of a theorem using automated solvers?▼

You can verify theorem soundness by leveraging the Z3 solver to check induction principles and validate specific steps of your mathematical logic proofs systematically.

What is the best way to choose a proof strategy for mathematical logic problems?▼

Selecting a proof strategy involves guiding your approach through direct proof, proof by contradiction, proof by cases, or induction based on the specific structure of your theorem.

How do I structure a mathematical induction proof correctly?▼

Structuring mathematical induction proofs requires applying systematic reasoning strategies, using available tools to verify the base case and inductive steps for soundness.

Can I use Z3 solver for formal verification of mathematical logic?▼

Yes, Z3 solver supports formal verification within mathematical logic by providing automated assistance for induction principles and verifying the soundness of constructed proofs.

Do I need prerequisite tools to perform formal theorem proving?▼

Performing formal theorem proving benefits from math scratchpad dependencies to manage intermediate calculations while using Z3 solver for verifying logical consistency.

What are the limitations of automated proof verification for complex theorems?▼

Automated proof verification assists with soundness checks and specific steps, but complex theorems still require manual strategy selection between direct proof, contradiction, cases, or induction.