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