Update dim. 27 août 2023 14:50:03 EDT

Changes

67 changed files (+66/-66)

• MIL/C01_Introduction/S02_Overview.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.Basic import Mathlib.Data.Nat.Parity - import Mathlib.Tactic + import MIL.Common open Nat
• MIL/C01_Introduction/solutions/Solutions_S02_Overview.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.Basic import Mathlib.Data.Nat.Parity - import Mathlib.Tactic + import MIL.Common open Nat
• MIL/C02_Basics/S01_Calculating.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic -- An example. example (a b c : ℝ) : a * b * c = b * (a * c) := by
• MIL/C02_Basics/S02_Proving_Identities_in_Algebraic_Structures.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Algebra.Ring.Defs import Mathlib.Data.Real.Basic - import Mathlib.Tactic + import MIL.Common section variable (R : Type*) [Ring R]
• MIL/C02_Basics/S03_Using_Theorems_and_Lemmas.lean
  • @@ -1,5 +1,5 @@
    import Mathlib.Analysis.SpecialFunctions.Log.Basic - import Mathlib.Tactic + import MIL.Common variable (a b c d e : ℝ) open Real
• MIL/C02_Basics/S04_More_on_Order_and_Divisibility.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C02S04
• MIL/C02_Basics/S05_Proving_Facts_about_Algebraic_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.MetricSpace.Basic section
• MIL/C02_Basics/solutions/Solutions_S01_Calculating.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic example (a b c : ℝ) : c * b * a = b * (a * c) := by rw [mul_comm c b]
• MIL/C02_Basics/solutions/Solutions_S02_Proving_Identities_in_Algebraic_Structures.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Algebra.Ring.Defs import Mathlib.Data.Real.Basic - import Mathlib.Tactic + import MIL.Common namespace MyRing variable {R : Type*} [Ring R]
• MIL/C02_Basics/solutions/Solutions_S03_Using_Theorems_and_Lemmas.lean
  • @@ -1,5 +1,5 @@
    import Mathlib.Analysis.SpecialFunctions.Log.Basic - import Mathlib.Tactic + import MIL.Common variable (a b c d e : ℝ) open Real
• MIL/C02_Basics/solutions/Solutions_S04_More_on_Order_and_Divisibility.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C02S04
• MIL/C02_Basics/solutions/Solutions_S05_Proving_Facts_about_Algebraic_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.MetricSpace.Basic section
• MIL/C03_Logic/S01_Implication_and_the_Universal_Quantifier.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S01
• MIL/C03_Logic/S02_The_Existential_Quantifier.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S02
• MIL/C03_Logic/S03_Negation.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S03
• MIL/C03_Logic/S04_Conjunction_and_Iff.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic import Mathlib.Data.Nat.Prime
• MIL/C03_Logic/S05_Disjunction.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S05
• MIL/C03_Logic/S06_Sequences_and_Convergence.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S06
• MIL/C03_Logic/solutions/Solutions_S01_Implication_and_the_Universal_Quantifier.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S01
• MIL/C03_Logic/solutions/Solutions_S02_The_Existential_Quantifier.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S02
• MIL/C03_Logic/solutions/Solutions_S03_Negation.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S03
• MIL/C03_Logic/solutions/Solutions_S04_Conjunction_and_Iff.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic import Mathlib.Data.Nat.Prime
• MIL/C03_Logic/solutions/Solutions_S05_Disjunction.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S05
• MIL/C03_Logic/solutions/Solutions_S06_Sequences_and_Convergence.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C03S06
• MIL/C04_Sets_and_Functions/S01_Sets.lean
  • @@ -1,7 +1,7 @@
    import Mathlib.Data.Set.Lattice import Mathlib.Data.Nat.Prime import Mathlib.Data.Nat.Parity - import Mathlib.Tactic + import MIL.Common section variable {α : Type*}
• MIL/C04_Sets_and_Functions/S02_Functions.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function import Mathlib.Analysis.SpecialFunctions.Log.Basic
• MIL/C04_Sets_and_Functions/S03_The_Schroeder_Bernstein_Theorem.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function - import Mathlib.Tactic + import MIL.Common open Set open Function
• MIL/C04_Sets_and_Functions/solutions/Solutions_S01_Sets.lean
  • @@ -1,7 +1,7 @@
    import Mathlib.Data.Set.Lattice import Mathlib.Data.Nat.Prime import Mathlib.Data.Nat.Parity - import Mathlib.Tactic + import MIL.Common section variable {α : Type*}
• MIL/C04_Sets_and_Functions/solutions/Solutions_S02_Functions.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function import Mathlib.Analysis.SpecialFunctions.Log.Basic
• MIL/C04_Sets_and_Functions/solutions/Solutions_S03_The_Schroeder_Bernstein_Theorem.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function - import Mathlib.Tactic + import MIL.Common open Set open Function
• MIL/C05_Elementary_Number_Theory/S01_Irrational_Roots.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Nat.Factorization.Basic import Mathlib.Data.Nat.Prime
• MIL/C05_Elementary_Number_Theory/S02_Induction_and_Recursion.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.GCD.Basic import Mathlib.Algebra.BigOperators.Basic - import Mathlib.Tactic + import MIL.Common example (n : Nat) : n.succ ≠ Nat.zero := Nat.succ_ne_zero n
• MIL/C05_Elementary_Number_Theory/S03_Infinitely_Many_Primes.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.Prime import Mathlib.Algebra.BigOperators.Order - import Mathlib.Tactic + import MIL.Common open BigOperators
• MIL/C05_Elementary_Number_Theory/solutions/Solutions_S01_Irrational_Roots.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Nat.Factorization.Basic import Mathlib.Data.Nat.Prime
• MIL/C05_Elementary_Number_Theory/solutions/Solutions_S02_Induction_and_Recursion.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.GCD.Basic import Mathlib.Algebra.BigOperators.Basic - import Mathlib.Tactic + import MIL.Common def fac : ℕ → ℕ | 0 => 1
• MIL/C05_Elementary_Number_Theory/solutions/Solutions_S03_Infinitely_Many_Primes.lean
  • @@ -1,6 +1,6 @@
    import Mathlib.Data.Nat.Prime import Mathlib.Algebra.BigOperators.Order - import Mathlib.Tactic + import MIL.Common open BigOperators
• MIL/C06_Structures/S01_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C06_Structures/S02_Algebraic_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C06S02
• MIL/C06_Structures/S03_Building_the_Gaussian_Integers.lean
  • @@ -1,7 +1,7 @@
    import Mathlib.Data.Int.Basic import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.RingTheory.PrincipalIdealDomain - import Mathlib.Tactic + import MIL.Common @[ext] structure gaussInt where
• MIL/C06_Structures/solutions/Solutions_S01_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C06_Structures/solutions/Solutions_S02_Algebraic_Structures.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Data.Real.Basic namespace C06S02
• MIL/C06_Structures/solutions/Solutions_S03_Building_the_Gaussian_Integers.lean
  • @@ -1,7 +1,7 @@
    import Mathlib.Data.Int.Basic import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.RingTheory.PrincipalIdealDomain - import Mathlib.Tactic + import MIL.Common @[ext] structure gaussInt where
• MIL/C07_Hierarchies/S01_Basics.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic.LibrarySearch + import MIL.Common import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C07_Hierarchies/S02_Morphisms.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real
• MIL/C07_Hierarchies/S03_Subobjects.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.GroupTheory.QuotientGroup
• MIL/C07_Hierarchies/solutions/Solutions_S01_Basics.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic.LibrarySearch + import MIL.Common import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C07_Hierarchies/solutions/Solutions_S02_Morphisms.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real
• MIL/C07_Hierarchies/solutions/Solutions_S03_Subobjects.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.GroupTheory.QuotientGroup
• MIL/C08_Topology/S01_Filters.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real open Set Filter Topology
• MIL/C08_Topology/S02_Metric_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C08_Topology/S03_Topological_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C08_Topology/solutions/Solutions_S01_Filters.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real open Set Filter Topology
• MIL/C08_Topology/solutions/Solutions_S02_Metric_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C08_Topology/solutions/Solutions_S03_Topological_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C09_Differential_Calculus/S01_Elementary_Differential_Calculus.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.MeanValue
• MIL/C09_Differential_Calculus/S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse
• MIL/C09_Differential_Calculus/solutions/Solutions_S01_Elementary_Differential_Calculus.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.Calculus.Deriv.Pow import Mathlib.Analysis.Calculus.MeanValue
• MIL/C09_Differential_Calculus/solutions/Solutions_S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse
• MIL/C10_Integration_and_Measure_Theory/S01_Elementary_Integration.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.MeasureTheory.Integral.IntervalIntegral import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Analysis.Convolution
• MIL/C10_Integration_and_Measure_Theory/S02_Measure_Theory.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• MIL/C10_Integration_and_Measure_Theory/S03_Integration.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S01_Elementary_Integration.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.MeasureTheory.Integral.IntervalIntegral import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Analysis.Convolution
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S02_Measure_Theory.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S03_Integration.lean
  • @@ -1,4 +1,4 @@
    - import Mathlib.Tactic + import MIL.Common import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• html/C02_Basics.html
  • @@ -370,7 +370,7 @@ import <code class="docutils literal notranslate"><span class="pre">Mathlib.Data
    but we will see in the next section that it can be used for calculations on structures other than the real numbers. It can be imported explicitly with the command - <code class="docutils literal notranslate"><span class="pre">import</span> <span class="pre">Mathlib.Tactic</span></code>. + <code class="docutils literal notranslate"><span class="pre">import</span> <span class="pre">MIL.Tactic</span></code>. We will see there are similar tactics for other common kind of algebraic structures.</p> <p>There is a variation of <code class="docutils literal notranslate"><span class="pre">rw</span></code> called <code class="docutils literal notranslate"><span class="pre">nth_rewrite</span></code> that allows you to replace only particular instances of an expression in the goal.
• html/searchindex.js
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    - 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class=\"section-number\">1. </span>Introduction","<span class=\"section-number\">2. </span>Basics","<span class=\"section-number\">3. </span>Logic","<span class=\"section-number\">4. </span>Sets and Functions","<span class=\"section-number\">5. </span>Elementary Number Theory","<span class=\"section-number\">6. </span>Structures","<span class=\"section-number\">7. </span>Hierarchies","<span class=\"section-number\">8. </span>Topology","<span class=\"section-number\">9. </span>Differential Calculus","<span class=\"section-number\">10. </span>Integration and Measure Theory","Index","Mathematics in Lean"],titleterms:{"function":[3,7],"schr\u00f6der":3,The:[2,3],about:1,algebra:[1,5],appli:1,asymptot:8,ball:7,basic:[1,6],bernstein:3,build:5,calcul:1,calculu:8,close:7,compact:7,comparison:8,complet:7,conjunct:2,continu:[7,8],converg:[2,7],countabl:7,defin:5,differenti:8,disjunct:2,elementari:[4,8,9],exampl:1,existenti:2,fact:1,filter:7,fundament:7,gaussian:5,get:0,hierarchi:6,ident:1,iff:2,implic:2,index:10,induct:4,infinit:4,integ:5,integr:9,introduct:0,irrat:4,lean:11,lemma:1,linear:8,logic:2,mani:4,map:8,mathemat:11,measur:9,metric:7,more:1,morphism:6,negat:2,norm:8,number:4,object:6,open:7,overview:0,prime:4,prove:1,quantifi:2,recurs:4,root:4,rw:1,separ:7,sequenc:2,set:[3,7],space:[7,8],start:0,structur:[1,5],sub:6,theorem:[1,3],theori:[4,9],topolog:7,uniformli:7,univers:2,us:1}}) + 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class=\"section-number\">1. </span>Introduction","<span class=\"section-number\">2. </span>Basics","<span class=\"section-number\">3. </span>Logic","<span class=\"section-number\">4. </span>Sets and Functions","<span class=\"section-number\">5. </span>Elementary Number Theory","<span class=\"section-number\">6. </span>Structures","<span class=\"section-number\">7. </span>Hierarchies","<span class=\"section-number\">8. </span>Topology","<span class=\"section-number\">9. </span>Differential Calculus","<span class=\"section-number\">10. </span>Integration and Measure Theory","Index","Mathematics in Lean"],titleterms:{"function":[3,7],"schr\u00f6der":3,The:[2,3],about:1,algebra:[1,5],appli:1,asymptot:8,ball:7,basic:[1,6],bernstein:3,build:5,calcul:1,calculu:8,close:7,compact:7,comparison:8,complet:7,conjunct:2,continu:[7,8],converg:[2,7],countabl:7,defin:5,differenti:8,disjunct:2,elementari:[4,8,9],exampl:1,existenti:2,fact:1,filter:7,fundament:7,gaussian:5,get:0,hierarchi:6,ident:1,iff:2,implic:2,index:10,induct:4,infinit:4,integ:5,integr:9,introduct:0,irrat:4,lean:11,lemma:1,linear:8,logic:2,mani:4,map:8,mathemat:11,measur:9,metric:7,more:1,morphism:6,negat:2,norm:8,number:4,object:6,open:7,overview:0,prime:4,prove:1,quantifi:2,recurs:4,root:4,rw:1,separ:7,sequenc:2,set:[3,7],space:[7,8],start:0,structur:[1,5],sub:6,theorem:[1,3],theori:[4,9],topolog:7,uniformli:7,univers:2,us:1}})
• mathematics_in_lean.pdf