Mathematics in Lean
1. イントロダクション
2. 基礎
3. 論理
4. Sets and Functions
5. Elementary Number Theory
6. Structures
7. Hierarchies
8. Topology
9. Differential Calculus
10. Integration and Measure Theory
Index
Mathematics in Lean
Mathematics in Lean
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Mathematics in Lean
1. イントロダクション
1.1. 本書の始め方
1.2. 概要
2. 基礎
2.1. 計算
2.2. 代数的構造における等式の証明
2.3. 定理と補題を使う
2.4. applyとrwをさらに活用する
2.5. 代数構造についての事実の証明
3. 論理
3.1. Implication and the Universal Quantifier
3.2. The Existential Quantifier
3.3. Negation
3.4. Conjunction and Iff
3.5. Disjunction
3.6. Sequences and Convergence
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
6. Structures
6.1. Defining structures
6.2. Algebraic Structures
6.3. Building the Gaussian Integers
7. Hierarchies
7.1. Basics
7.2. Morphisms
7.3. Sub-objects
8. Topology
8.1. Filters
8.2. Metric spaces
8.3. Topological spaces
9. Differential Calculus
9.1. Elementary Differential Calculus
9.2. Differential Calculus in Normed Spaces
10. Integration and Measure Theory
10.1. Elementary Integration
10.2. Measure Theory
10.3. Integration