# Theorem Proving

> Construct and verify mathematical proofs using LaTeX typesetting and computational verification via jupyter_execute

- Skill: `zaoqu-liu/theorem-proving` (Agent Skill)
- Install (CLI): `npx skillmds@latest add zaoqu-liu/theorem-proving`
- Raw SKILL.md: https://api.skillmd.com/api/skills/zaoqu-liu/theorem-proving/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: zaoqu-liu (https://skillmd.com/u/zaoqu-liu)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/zaoqu-liu/theorem-proving

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# Theorem Proving Skill

## Description
Assist with constructing, verifying, and typesetting mathematical proofs. Combines rigorous logical reasoning with computational verification.

## Tools Used
- `latex_compile` - Typeset proofs and mathematical documents (auto-switches to LaTeX editor)
- `update_latex` - Write LaTeX content to the editor for review before compiling
- `jupyter_execute` - Verify results computationally (sympy, numpy)
- `update_notes` - Write proof outlines and scratch work to Notes editor

## Capabilities

### Proof Construction
- Direct proofs, proof by contradiction, proof by induction
- Constructive and non-constructive existence proofs
- Epsilon-delta arguments in analysis
- Diagram chasing in algebra/category theory

### Verification
- Symbolic computation to check algebraic manipulations
- Numerical examples to build intuition
- Counterexample search for false conjectures
- Automated checking of special cases

### Typesetting
- AMS theorem environments (theorem, lemma, proposition, corollary, definition)
- Proper mathematical notation and spacing
- Cross-references and equation numbering
- Multi-part proofs with clear structure

## Usage Patterns

### Prove a Theorem
When user says: "Prove that [statement]"
1. Clarify definitions and assumptions
2. Outline proof strategy
3. Construct formal proof step-by-step
4. Verify key steps computationally if possible
5. Typeset in LaTeX with proper environments

### Verify a Conjecture
When user says: "Is it true that [conjecture]?"
1. Test with specific examples (jupyter_execute)
2. Search for counterexamples
3. Attempt proof if examples support it
4. Report findings with confidence level