Mathematics in Lean

• 1. Introduction
  • 1.1. Getting Started
  • 1.2. Overview
• 2. Basics
  • 2.1. Calculating Proof Steps via Rewriting
  • 2.2. Proving Basic Identities in Ring Algebraic Structure
  • 2.3. Using Theorems and Lemmas
  • 2.4. min, max, ∣, .gcd, .lcm
  • 2.5. Proving Facts about Algebraic Structures
• 3. Logic
  • 3.1. Universal Quantifier ∀ and intro
  • 3.2. The Existential Quantifier
  • 3.3. Proving Statements of Negation: Counterexample, by_contra, push_neg, contrapose
  • 3.4. Proving and Using Conjunction
  • 3.5. Disjunction
  • 3.6. Sequences and Functional Equality
• 4. Sets and Functions
  • 4.1. Sets
  • 4.2. Functions
  • 4.3. The Schröder-Bernstein Theorem
• 5. Elementary Number Theory
  • 5.1. Irrational Roots
  • 5.2. Induction and Recursion
  • 5.3. Infinitely Many Primes
  • 5.4. More Induction
• 6. Discrete Mathematics
  • 6.1. Finsets and Fintypes
  • 6.2. Counting Arguments
  • 6.3. Inductively Defined Types
• 7. Structures
  • 7.1. Structures
  • 7.2. Algebraic Structures
  • 7.3. Building the Gaussian Integers
• 8. Hierarchies
  • 8.1. Basics
  • 8.2. Morphisms
  • 8.3. Sub-objects
• 9. Groups and Rings
  • 9.1. Monoids and Groups
  • 9.2. Rings
• 10. Linear algebra
  • 10.1. Vector spaces and linear maps
  • 10.2. Subspaces
  • 10.3. Endomorphisms
  • 10.4. Matrices, bases and dimension
• 11. Topology
  • 11.1. Filters
  • 11.2. Metric spaces
  • 11.3. Topological spaces
• 12. Differential Calculus
  • 12.1. Elementary Differential Calculus
  • 12.2. Differential Calculus in Normed Spaces
• 13. Integration and Measure Theory
  • 13.1. Elementary Integration
  • 13.2. Measure Theory
  • 13.3. Integration