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Maths Proofs in Lean: First Steps
This book is written specifically for anyone who wants to get started writing maths proofs with Lean, but is finding other courses and tutorials difficult.
This course is designed to provide a gentle path from knowing nothing about proof assistants to writing simple proofs in Lean, and developing the confidence to learn more.
Each chapter starts with a simple mathematical task, followed by a short discussion of how we might solve it with pen and paper, before providing a bite-sized Lean proof and a discussion of how the code works.
Each chapter introduces a specific new idea, and an exercise at the end of the chapter provides an opportunity to practice that idea. These exercises are also intentionally not difficult. The idea is to build confidence, not to demolish it.
The four parts of the book I - very simple direct proofs using arithmetic, substitution, algebra and inequalities.Part II - proofs with some structure, dealing with proof by cases, conjunction and disjunction, and existence proofs.Part II - using Mathlib's lemmas and definitions, and writing your own.Part IV - proof by contradiction, induction and recursively defined functions.
By the end of the course you will be experienced enough to write simple proofs, and more importantly, have the confidence and knowledge to go on to learn more advanced topics.
This course is designed to provide a gentle path from knowing nothing about proof assistants to writing simple proofs in Lean, and developing the confidence to learn more.
Each chapter starts with a simple mathematical task, followed by a short discussion of how we might solve it with pen and paper, before providing a bite-sized Lean proof and a discussion of how the code works.
Each chapter introduces a specific new idea, and an exercise at the end of the chapter provides an opportunity to practice that idea. These exercises are also intentionally not difficult. The idea is to build confidence, not to demolish it.
The four parts of the book I - very simple direct proofs using arithmetic, substitution, algebra and inequalities.Part II - proofs with some structure, dealing with proof by cases, conjunction and disjunction, and existence proofs.Part II - using Mathlib's lemmas and definitions, and writing your own.Part IV - proof by contradiction, induction and recursively defined functions.
By the end of the course you will be experienced enough to write simple proofs, and more importantly, have the confidence and knowledge to go on to learn more advanced topics.
147 pages, Hardcover
Published February 8, 2025
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