Theorem Proving

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