Contents

Introduction

• 00 - Proofs & Proof Assistants

Direct Proofs

• 01 - First Proof
• 02 - Substitution
• 03 - Symbols, No Numbers
• 04 - Simple Algebra
• 05 - Inequalities

Structured Proofs

• 06 - Intermediate Results
• 07 - Proof By Cases
• 08 - "And" Hypothesis
• 09 - "Or" Goal
• 10 - "And" Goal
• 11 - Existence

Definitions & Lemmas

• 12 - Odd & Even
• 13 - Disequality
• 14 - Disequality Again
• 15 - Zero Product
• 16 - Writing Our Own Lemma
• 17 - Using Our Own Lemma
• 18 - Our Own Definition

Interesting Proofs

• 19 - Reductio Ad Absurdum
• 20 - Contradictory Cases
• 21 - Simple Induction
• 22 - Recursion

Appendices

• Appendix A - Taxonomy
• Appendix B - Libraries