Merge pull request #15 from Lean-zh/c06

C06

1.ps1

@@ -0,0 +1,8 @@
+# 运行clean.py脚本
+python .\scripts\clean.py
+
+# 运行mkall.py脚本
+python .\scripts\mkall.py
+
+# html
+ sphinx-build source build

MIL.lean

@@ -1,40 +1,40 @@
-import MIL.C01_Introduction.S01_Getting_Started
-import MIL.C01_Introduction.S02_Overview
-import MIL.C02_Basics.S01_Calculating
-import MIL.C02_Basics.S02_Proving_Identities_in_Algebraic_Structures
-import MIL.C02_Basics.S03_Using_Theorems_and_Lemmas
-import MIL.C02_Basics.S04_More_on_Order_and_Divisibility
-import MIL.C02_Basics.S05_Proving_Facts_about_Algebraic_Structures
-import MIL.C03_Logic.S01_Implication_and_the_Universal_Quantifier
-import MIL.C03_Logic.S02_The_Existential_Quantifier
-import MIL.C03_Logic.S03_Negation
-import MIL.C03_Logic.S04_Conjunction_and_Iff
-import MIL.C03_Logic.S05_Disjunction
-import MIL.C03_Logic.S06_Sequences_and_Convergence
-import MIL.C04_Sets_and_Functions.S01_Sets
-import MIL.C04_Sets_and_Functions.S02_Functions
-import MIL.C04_Sets_and_Functions.S03_The_Schroeder_Bernstein_Theorem
-import MIL.C05_Elementary_Number_Theory.S01_Irrational_Roots
-import MIL.C05_Elementary_Number_Theory.S02_Induction_and_Recursion
-import MIL.C05_Elementary_Number_Theory.S03_Infinitely_Many_Primes
-import MIL.C06_Structures.S01_Structures
-import MIL.C06_Structures.S02_Algebraic_Structures
-import MIL.C06_Structures.S03_Building_the_Gaussian_Integers
-import MIL.C07_Hierarchies.S01_Basics
-import MIL.C07_Hierarchies.S02_Morphisms
-import MIL.C07_Hierarchies.S03_Subobjects
-import MIL.C08_Groups_and_Rings.S01_Groups
-import MIL.C08_Groups_and_Rings.S02_Rings
-import MIL.C09_Linear_Algebra.S01_Vector_Spaces
-import MIL.C09_Linear_Algebra.S02_Subspaces
-import MIL.C09_Linear_Algebra.S03_Endomorphisms
-import MIL.C09_Linear_Algebra.S04_Bases
-import MIL.C10_Topology.S01_Filters
-import MIL.C10_Topology.S02_Metric_Spaces
-import MIL.C10_Topology.S03_Topological_Spaces
-import MIL.C11_Differential_Calculus.S01_Elementary_Differential_Calculus
-import MIL.C11_Differential_Calculus.S02_Differential_Calculus_in_Normed_Spaces
-import MIL.C12_Integration_and_Measure_Theory.S01_Elementary_Integration
-import MIL.C12_Integration_and_Measure_Theory.S02_Measure_Theory
-import MIL.C12_Integration_and_Measure_Theory.S03_Integration
-import MIL.Common
+import MIL.C01_Introduction.S01_Getting_Started
+import MIL.C01_Introduction.S02_Overview
+import MIL.C02_Basics.S01_Calculating
+import MIL.C02_Basics.S02_Proving_Identities_in_Algebraic_Structures
+import MIL.C02_Basics.S03_Using_Theorems_and_Lemmas
+import MIL.C02_Basics.S04_More_on_Order_and_Divisibility
+import MIL.C02_Basics.S05_Proving_Facts_about_Algebraic_Structures
+import MIL.C03_Logic.S01_Implication_and_the_Universal_Quantifier
+import MIL.C03_Logic.S02_The_Existential_Quantifier
+import MIL.C03_Logic.S03_Negation
+import MIL.C03_Logic.S04_Conjunction_and_Iff
+import MIL.C03_Logic.S05_Disjunction
+import MIL.C03_Logic.S06_Sequences_and_Convergence
+import MIL.C04_Sets_and_Functions.S01_Sets
+import MIL.C04_Sets_and_Functions.S02_Functions
+import MIL.C04_Sets_and_Functions.S03_The_Schroeder_Bernstein_Theorem
+import MIL.C05_Elementary_Number_Theory.S01_Irrational_Roots
+import MIL.C05_Elementary_Number_Theory.S02_Induction_and_Recursion
+import MIL.C05_Elementary_Number_Theory.S03_Infinitely_Many_Primes
+import MIL.C06_Structures.S01_Structures
+import MIL.C06_Structures.S02_Algebraic_Structures
+import MIL.C06_Structures.S03_Building_the_Gaussian_Integers
+import MIL.C07_Hierarchies.S01_Basics
+import MIL.C07_Hierarchies.S02_Morphisms
+import MIL.C07_Hierarchies.S03_Subobjects
+import MIL.C08_Groups_and_Rings.S01_Groups
+import MIL.C08_Groups_and_Rings.S02_Rings
+import MIL.C09_Linear_Algebra.S01_Vector_Spaces
+import MIL.C09_Linear_Algebra.S02_Subspaces
+import MIL.C09_Linear_Algebra.S03_Endomorphisms
+import MIL.C09_Linear_Algebra.S04_Bases
+import MIL.C10_Topology.S01_Filters
+import MIL.C10_Topology.S02_Metric_Spaces
+import MIL.C10_Topology.S03_Topological_Spaces
+import MIL.C11_Differential_Calculus.S01_Elementary_Differential_Calculus
+import MIL.C11_Differential_Calculus.S02_Differential_Calculus_in_Normed_Spaces
+import MIL.C12_Integration_and_Measure_Theory.S01_Elementary_Integration
+import MIL.C12_Integration_and_Measure_Theory.S02_Measure_Theory
+import MIL.C12_Integration_and_Measure_Theory.S03_Integration
+import MIL.Common

MIL/C06_Structures/C06_Structures.rst

@@ -1,25 +1,16 @@
 .. _structures:
 
-Structures
-==========
+结构体（Structures）
+=========================
 
-Modern mathematics makes essential use of algebraic
-structures,
-which encapsulate patterns that can be instantiated in
-multiple settings.
-The subject provides various ways of defining such structures and
-constructing particular instances.
+现代数学广泛使用了代数结构，这些代数结构封装了可在不同环境中实例化的模式，而且往往有多种方法来对它们进行定义和实例化。
 
-Lean therefore provides corresponding ways of
-defining structures formally and working with them.
-You have already seen examples of algebraic structures in Lean,
-such as rings and lattices, which were discussed in
-:numref:`Chapter %s <basics>`.
-This chapter will explain the mysterious square bracket annotations
-that you saw there,
-``[Ring α]`` and ``[Lattice α]``.
-It will also show you how to define and use
-algebraic structures on your own.
+因此，Lean 提供了相应的方法来形式化定义这些结构并对其进行操作。
+此前你已经接触过一些代数结构的示例，比如在
+:numref:`Chapter %s <basics>`
+中的环（rings）和格（lattices）。
+本章将解释之前出现过的方括号语法，比如 ``[Ring α]``、 ``[Lattice α]``，并介绍如何创建和使用自定义的代数结构。
 
-For more technical detail, you can consult `Theorem Proving in Lean <https://leanprover.github.io/theorem_proving_in_lean/>`_,
-and a paper by Anne Baanen, `Use and abuse of instance parameters in the Lean mathematical library <https://arxiv.org/abs/2202.01629>`_.
+如需了解更多技术细节，可以参考
+`Theorem Proving in Lean <https://leanprover.github.io/theorem_proving_in_lean/>`_，
+以及 Anne Baanen 的这篇论文 `Use and abuse of instance parameters in the Lean mathematical library <https://arxiv.org/abs/2202.01629>`_。

MIL/C06_Structures/C06_Structures.rst.backup

@@ -0,0 +1,25 @@
+.. _structures:
+
+Structures
+==========
+
+Modern mathematics makes essential use of algebraic
+structures,
+which encapsulate patterns that can be instantiated in
+multiple settings.
+The subject provides various ways of defining such structures and
+constructing particular instances.
+
+Lean therefore provides corresponding ways of
+defining structures formally and working with them.
+You have already seen examples of algebraic structures in Lean,
+such as rings and lattices, which were discussed in
+:numref:`Chapter %s <basics>`.
+This chapter will explain the mysterious square bracket annotations
+that you saw there,
+``[Ring α]`` and ``[Lattice α]``.
+It will also show you how to define and use
+algebraic structures on your own.
+
+For more technical detail, you can consult `Theorem Proving in Lean <https://leanprover.github.io/theorem_proving_in_lean/>`_,
+and a paper by Anne Baanen, `Use and abuse of instance parameters in the Lean mathematical library <https://arxiv.org/abs/2202.01629>`_.