Update lun. 04 déc. 2023 10:45:23 EST

Changes

17 changed files (+86/-79)

• MIL/C05_Elementary_Number_Theory/S03_Infinitely_Many_Primes.lean
  • @@ -164,7 +164,7 @@ theorem mod_4_eq_3_or_mod_4_eq_3 {m n : ℕ} (h : m * n % 4 = 3) : m % 4 = 3 ∨
    have : m % 4 < 4 := Nat.mod_lt m (by norm_num) interval_cases hm : m % 4 <;> simp [hm] have : n % 4 < 4 := Nat.mod_lt n (by norm_num) - interval_cases hn : n % 4 <;> simp [hn] + interval_cases hn : n % 4 <;> simp [hn] ; decide theorem two_le_of_mod_4_eq_3 {n : ℕ} (h : n % 4 = 3) : 2 ≤ n := by apply two_le <;>
• MIL/C05_Elementary_Number_Theory/solutions/Solutions_S03_Infinitely_Many_Primes.lean
  • @@ -150,7 +150,7 @@ theorem mod_4_eq_3_or_mod_4_eq_3 {m n : ℕ} (h : m * n % 4 = 3) : m % 4 = 3 ∨
    have : m % 4 < 4 := Nat.mod_lt m (by norm_num) interval_cases hm : m % 4 <;> simp [hm] have : n % 4 < 4 := Nat.mod_lt n (by norm_num) - interval_cases hn : n % 4 <;> simp [hn] + interval_cases hn : n % 4 <;> simp [hn] ; decide theorem two_le_of_mod_4_eq_3 {n : ℕ} (h : n % 4 = 3) : 2 ≤ n := by apply two_le <;>
• MIL/C08_Groups_and_Rings/S01_Groups.lean
  • @@ -191,6 +191,7 @@ lemma compat_myMap :
    ∀ r ∈ ({.of () ^ 3} : Set (FreeGroup Unit)), FreeGroup.lift myMap r = 1 := by rintro _ rfl simp + decide def myNewMorphism : myGroup →* Perm (Fin 5) := PresentedGroup.toGroup compat_myMap
• MIL/C09_Topology/S03_Topological_Spaces.lean
  • @@ -115,7 +115,7 @@ example [TopologicalSpace X] [TopologicalSpace Y] [T3Space Y] {A : Set X}
    #check HasBasis.tendsto_right_iff - example [TopologicalSpace X] [TopologicalSpace.FirstCountableTopology X] + example [TopologicalSpace X] [FirstCountableTopology X] {s : Set X} {a : X} : a ∈ closure s ↔ ∃ u : ℕ → X, (∀ n, u n ∈ s) ∧ Tendsto u atTop (𝓝 a) := mem_closure_iff_seq_limit
  • @@ -129,7 +129,7 @@ example {s : Set X} :
    IsCompact s ↔ ∀ (F : Filter X) [NeBot F], F ≤ 𝓟 s → ∃ a ∈ s, ClusterPt a F := Iff.rfl - example [TopologicalSpace.FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) + example [FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) (hu : ∀ n, u n ∈ s) : ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := hs.tendsto_subseq hu
• MIL/C09_Topology/solutions/Solutions_S03_Topological_Spaces.lean
  • @@ -139,7 +139,7 @@ example [TopologicalSpace X] [TopologicalSpace Y] [T3Space Y] {A : Set X}
    have lim : Tendsto f (𝓝 a) (𝓝 (φ a)) := by simpa [nhds_induced] using hφ a exact tendsto_nhds_unique lim f_cont.continuousAt - example [TopologicalSpace X] [TopologicalSpace.FirstCountableTopology X] + example [TopologicalSpace X] [FirstCountableTopology X] {s : Set X} {a : X} : a ∈ closure s ↔ ∃ u : ℕ → X, (∀ n, u n ∈ s) ∧ Tendsto u atTop (𝓝 a) := mem_closure_iff_seq_limit
  • @@ -153,7 +153,7 @@ example {s : Set X} :
    IsCompact s ↔ ∀ (F : Filter X) [NeBot F], F ≤ 𝓟 s → ∃ a ∈ s, ClusterPt a F := Iff.rfl - example [TopologicalSpace.FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) + example [FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) (hu : ∀ n, u n ∈ s) : ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := hs.tendsto_subseq hu
• MIL/C10_Differential_Calculus/S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -2,7 +2,7 @@ import MIL.Common
    import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse - import Mathlib.Analysis.Calculus.ContDiff + import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.FDeriv.Prod
• MIL/C10_Differential_Calculus/solutions/Solutions_S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -2,7 +2,7 @@ import MIL.Common
    import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse - import Mathlib.Analysis.Calculus.ContDiff + import Mathlib.Analysis.Calculus.ContDiff.Basic import Mathlib.Analysis.Calculus.FDeriv.Prod
• MIL/Common.lean
  • @@ -1,4 +1,4 @@
    import Mathlib.Tactic - import Mathlib.Util.PiNotation + import Mathlib.Util.Delaborators set_option warningAsError false
• html/C05_Elementary_Number_Theory.html
  • @@ -738,7 +738,7 @@ Remember that you can hover over it to see its documentation.</p>
    <span class="n">interval_cases</span> <span class="n">m</span> <span class="bp">&lt;;&gt;</span> <span class="n">contradiction</span> </pre></div> </div> - <p>Recall that the semicolon after <code class="docutils literal notranslate"><span class="pre">interval_cases</span> <span class="pre">m</span></code> means + <p id="index-0">Recall that the semicolon after <code class="docutils literal notranslate"><span class="pre">interval_cases</span> <span class="pre">m</span></code> means that the next tactic is applied to each of the cases that it generates. Yet another option is to use the tactic, <code class="docutils literal notranslate"><span class="pre">decide</span></code>, which tries to find a decision procedure to solve the problem.
  • @@ -1048,7 +1048,7 @@ that result from the application of <code class="docutils literal notranslate"><
    <span class="k">have</span> <span class="o">:</span> <span class="n">m</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">&lt;</span> <span class="mi">4</span> <span class="o">:=</span> <span class="n">Nat.mod_lt</span> <span class="n">m</span> <span class="o">(</span><span class="kd">by</span> <span class="n">norm_num</span><span class="o">)</span> <span class="n">interval_cases</span> <span class="n">hm</span> <span class="o">:</span> <span class="n">m</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">&lt;;&gt;</span> <span class="n">simp</span> <span class="o">[</span><span class="n">hm</span><span class="o">]</span> <span class="k">have</span> <span class="o">:</span> <span class="n">n</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">&lt;</span> <span class="mi">4</span> <span class="o">:=</span> <span class="n">Nat.mod_lt</span> <span class="n">n</span> <span class="o">(</span><span class="kd">by</span> <span class="n">norm_num</span><span class="o">)</span> - <span class="n">interval_cases</span> <span class="n">hn</span> <span class="o">:</span> <span class="n">n</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">&lt;;&gt;</span> <span class="n">simp</span> <span class="o">[</span><span class="n">hn</span><span class="o">]</span> + <span class="n">interval_cases</span> <span class="n">hn</span> <span class="o">:</span> <span class="n">n</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">&lt;;&gt;</span> <span class="n">simp</span> <span class="o">[</span><span class="n">hn</span><span class="o">]</span> <span class="bp">;</span> <span class="n">decide</span> <span class="kd">theorem</span> <span class="n">two_le_of_mod_4_eq_3</span> <span class="o">{</span><span class="n">n</span> <span class="o">:</span> <span class="n">&#8469;</span><span class="o">}</span> <span class="o">(</span><span class="n">h</span> <span class="o">:</span> <span class="n">n</span> <span class="bp">%</span> <span class="mi">4</span> <span class="bp">=</span> <span class="mi">3</span><span class="o">)</span> <span class="o">:</span> <span class="mi">2</span> <span class="bp">&#8804;</span> <span class="n">n</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">apply</span> <span class="n">two_le</span> <span class="bp">&lt;;&gt;</span>
• html/C08_Groups_and_Rings.html
  • @@ -485,6 +485,7 @@ to <code class="docutils literal notranslate"><span class="pre">PresentedGroup.t
    <span class="bp">&#8704;</span> <span class="n">r</span> <span class="bp">&#8712;</span> <span class="o">({</span><span class="bp">.</span><span class="n">of</span> <span class="o">()</span> <span class="bp">^</span> <span class="mi">3</span><span class="o">}</span> <span class="o">:</span> <span class="n">Set</span> <span class="o">(</span><span class="n">FreeGroup</span> <span class="n">Unit</span><span class="o">)),</span> <span class="n">FreeGroup.lift</span> <span class="n">myMap</span> <span class="n">r</span> <span class="bp">=</span> <span class="mi">1</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">rintro</span> <span class="n">_</span> <span class="n">rfl</span> <span class="n">simp</span> + <span class="n">decide</span> <span class="kd">def</span> <span class="n">myNewMorphism</span> <span class="o">:</span> <span class="n">myGroup</span> <span class="bp">&#8594;*</span> <span class="n">Perm</span> <span class="o">(</span><span class="n">Fin</span> <span class="mi">5</span><span class="o">)</span> <span class="o">:=</span> <span class="n">PresentedGroup.toGroup</span> <span class="n">compat_myMap</span>
• html/C09_Topology.html
  • @@ -1124,7 +1124,7 @@ together with the fact that <code class="docutils literal notranslate"><span cla
    space to bring it closer to metric spaces is countability assumption. The main one is first countability asking that every point has a countable neighborhood basic. In particular this ensures that closure of sets can be understood using sequences.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">[</span><span class="n">TopologicalSpace</span> <span class="n">X</span><span class="o">]</span> <span class="o">[</span><span class="n">TopologicalSpace.FirstCountableTopology</span> <span class="n">X</span><span class="o">]</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">[</span><span class="n">TopologicalSpace</span> <span class="n">X</span><span class="o">]</span> <span class="o">[</span><span class="n">FirstCountableTopology</span> <span class="n">X</span><span class="o">]</span> <span class="o">{</span><span class="n">s</span> <span class="o">:</span> <span class="n">Set</span> <span class="n">X</span><span class="o">}</span> <span class="o">{</span><span class="n">a</span> <span class="o">:</span> <span class="n">X</span><span class="o">}</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">&#8712;</span> <span class="n">closure</span> <span class="n">s</span> <span class="bp">&#8596;</span> <span class="bp">&#8707;</span> <span class="n">u</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">X</span><span class="o">,</span> <span class="o">(</span><span class="bp">&#8704;</span> <span class="n">n</span><span class="o">,</span> <span class="n">u</span> <span class="n">n</span> <span class="bp">&#8712;</span> <span class="n">s</span><span class="o">)</span> <span class="bp">&#8743;</span> <span class="n">Tendsto</span> <span class="n">u</span> <span class="n">atTop</span> <span class="o">(</span><span class="bp">&#120029;</span> <span class="n">a</span><span class="o">)</span> <span class="o">:=</span> <span class="n">mem_closure_iff_seq_limit</span>
  • @@ -1156,7 +1156,7 @@ large enough. Saying that <code class="docutils literal notranslate"><span class
    intersects the set of points that are close to <code class="docutils literal notranslate"><span class="pre">x</span></code>. In case <code class="docutils literal notranslate"><span class="pre">&#120029;</span> <span class="pre">x</span></code> has a countable basis, we can interpret this as saying that <code class="docutils literal notranslate"><span class="pre">u</span></code> has a subsequence converging to <code class="docutils literal notranslate"><span class="pre">x</span></code>, and we get back what compactness looks like in metric spaces.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">[</span><span class="n">TopologicalSpace.FirstCountableTopology</span> <span class="n">X</span><span class="o">]</span> <span class="o">{</span><span class="n">s</span> <span class="o">:</span> <span class="n">Set</span> <span class="n">X</span><span class="o">}</span> <span class="o">{</span><span class="n">u</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">X</span><span class="o">}</span> <span class="o">(</span><span class="n">hs</span> <span class="o">:</span> <span class="n">IsCompact</span> <span class="n">s</span><span class="o">)</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">[</span><span class="n">FirstCountableTopology</span> <span class="n">X</span><span class="o">]</span> <span class="o">{</span><span class="n">s</span> <span class="o">:</span> <span class="n">Set</span> <span class="n">X</span><span class="o">}</span> <span class="o">{</span><span class="n">u</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">X</span><span class="o">}</span> <span class="o">(</span><span class="n">hs</span> <span class="o">:</span> <span class="n">IsCompact</span> <span class="n">s</span><span class="o">)</span> <span class="o">(</span><span class="n">hu</span> <span class="o">:</span> <span class="bp">&#8704;</span> <span class="n">n</span><span class="o">,</span> <span class="n">u</span> <span class="n">n</span> <span class="bp">&#8712;</span> <span class="n">s</span><span class="o">)</span> <span class="o">:</span> <span class="bp">&#8707;</span> <span class="n">a</span> <span class="bp">&#8712;</span> <span class="n">s</span><span class="o">,</span> <span class="bp">&#8707;</span> <span class="n">&#966;</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">&#8469;</span><span class="o">,</span> <span class="n">StrictMono</span> <span class="n">&#966;</span> <span class="bp">&#8743;</span> <span class="n">Tendsto</span> <span class="o">(</span><span class="n">u</span> <span class="bp">&#8728;</span> <span class="n">&#966;</span><span class="o">)</span> <span class="n">atTop</span> <span class="o">(</span><span class="bp">&#120029;</span> <span class="n">a</span><span class="o">)</span> <span class="o">:=</span> <span class="n">hs.tendsto_subseq</span> <span class="n">hu</span> </pre></div>
• html/genindex.html
  • @@ -181,12 +181,14 @@
    <h2 id="D">D</h2> <table style="width: 100%" class="indextable genindextable"><tr> <td style="width: 33%; vertical-align: top;"><ul> - <li><a href="C02_Basics.html#index-13">definitional equality</a> + <li><a href="C05_Elementary_Number_Theory.html#index-0">decide</a> </li> - <li><a href="C10_Differential_Calculus.html#index-0">differential calculus</a> + <li><a href="C02_Basics.html#index-13">definitional equality</a> </li> </ul></td> <td style="width: 33%; vertical-align: top;"><ul> + <li><a href="C10_Differential_Calculus.html#index-0">differential calculus</a> + </li> <li><a href="C02_Basics.html#index-25">divisibility</a> </li> <li><a href="C03_Logic.html#index-2">dsimp</a>
  • @@ -451,6 +453,8 @@
    <li><a href="C03_Logic.html#index-16">contrapose</a> </li> <li><a href="C03_Logic.html#index-26">convert</a> + </li> + <li><a href="C05_Elementary_Number_Theory.html#index-0">decide</a> </li> <li><a href="C03_Logic.html#index-2">dsimp</a> </li>
• html/searchindex.js
  • @@ -1,1 +1,1 @@
    - 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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>Groups and Rings","<span class=\"section-number\">9. </span>Topology","<span class=\"section-number\">10. </span>Differential Calculus","<span class=\"section-number\">11. </span>Integration and Measure Theory","Index","Mathematics in 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2,3,4,5,7,8],togroup:7,tomuloneclass:6,too:[0,1,3,5,6,7,8],tool:[0,1,5,6],top:[0,6,7,8,9],topermhom:7,topic:[4,6,7],topolog:[1,5,6,9,12],topologicalspac:[8,9],toreal:10,total:1,tour:[8,9],toward:7,trace:6,tradeoff:3,tradition:7,train:[1,6],tran:[2,4,5,6,7],trans_assoc:5,trans_refl:5,transform:[2,3],transit:[1,2,5,8],translat:[4,6,7,8],trap:6,treat:[2,3,5,6,7,8,9],treatment:7,tri:[1,2,4,6],triangl:[1,2,5],trick:[1,2,4,6,9],tricki:[2,3,4,6,7],trigger:6,tripl:3,trivial:[3,4,7,8],troubl:[2,3,5],truncat:4,truth:[1,4],tupl:5,turn:[2,3,4,5,6,8,9],tutori:0,twice:[0,1,8],two:[0,1,2,3,4,5,6,7,8,10],two_l:4,two_le_of_mod_4_eq_3:4,two_mul:1,ty:7,type:[0,1,2,3,4,5,6,7,8,9,10],typeclass:6,typic:[1,7],u:[2,3,5,7,8,10],ubf:2,ubfa:2,ubg:2,ubgb:2,ulequiv:7,ultim:0,un:3,unbundl:6,unchang:[1,2],uncom:1,uncount:8,uncurri:8,under:[5,6,7,8],underli:[0,1,5,6,7],underneath:[1,3],underscor:[1,2,3],understand:[0,2,3,4,5,6,7,8],understood:[4,8],unfold:[1,2,3,4,5,8],unfortun:7,unicod:[1,3,6],unif:6,uniform:[3,8,9],uniformcontinu:8,uniformcontinuous_iff:8,uniformli:9,union:[1,3,4,5,6,7,9,10],union_def:3,uniqu:[1,2,3,4,5,7,8],unit:[5,6,8],units_eq_one_or:7,univ:[3,8,9,10],univ_set:8,univari:7,univers:[1,3,5,7,8,12],unknown:6,unless:[1,2,5],unlik:[3,4],unnecessari:[3,7],unpack:[2,3],unpleas:[6,8],unrel:6,unshad:3,unspecifi:6,unsurprisingli:3,until:[1,4,6,8],up:[0,2,3,4,5,6,7,8],updat:0,upper:[1,2],us:[0,2,3,4,5,6,7,8,9,10,12],usabl:6,usag:1,user:[0,6],usual:[1,2,3,4,5,7,8,10],v:[2,3,5,8],val:5,valid:2,valu:[1,2,3,4,5,6,7,8,9,10],van:0,vanish:7,varepsilon:[2,8],variabl:[1,2,3,4,5,6,7,8,9,10],variant:[1,2,7,8],variat:[1,3,4,5,8,9],varieti:8,variou:[2,3,5,6,10],vastli:2,ve:[6,8],vector:[1,3,6,7,9],verbatim:7,verbos:3,veri:[0,2,4,6,7,8,10],verifi:2,versa:[1,3],version:[0,1,2,3,4,5,6,7,8,9,10],vertic:[2,5],vi:5,via:8,vice:[1,3],view:[0,5,6,7,8],visibl:1,vocabulari:3,volum:10,vs:[0,1,2,3,5],w:[1,6],wa:[1,3,7],wai:[0,1,2,3,4,5,6,7,8,10],want:[0,1,2,3,4,5,6,7,8,9,10],wasn:8,we:[0,1,2,3,4,5,6,7,8,9,10],weak:6,weaker:[1,2],weav:5,web:[0,1,4],weight:5,weightedaverag:5,weird:[6,8],weirder:9,welcom:[0,1],well:[0,1,2,3,4,5,6,7,8],were:[2,4,5,8],what:[0,1,2,3,4,5,6,7,8],whatev:[0,2,4],whatsnew:6,when:[0,1,2,3,4,5,6,7,8,9],whenev:[1,2,4,5],where:[0,1,2,3,4,5,6,7,8,9,10],wherea:[0,1,2,3,5,7,8],wherebi:[5,8],whether:[1,2,3,4,6,8],which:[0,1,2,3,4,5,6,7,8,9,10],who:[0,8],whole:5,whose:[1,2,4,5,6,7,8,9],why:[0,2,4,6,7,8],wieser:0,window:[0,1,2,5],winston:0,wise:5,wish:8,withbot:7,within:[1,2,8],without:[1,2,4,5,6,7,8,9],withtop:9,wlog:3,won:[2,4,6,7,8],word:[1,2,3,4,5,7,8],work:[0,1,2,3,4,5,6,7,8,9],world:0,worri:[1,3,4,5,7],worth:[1,2,5],would:[1,2,3,4,5,6,7,8,9],wouldn:6,wrap:[6,8],write:[0,1,2,4,5,6,7,8,9,10],written:[1,2,3,4,5,6,7,8,9],wrong:3,wrote:4,x:[0,1,2,3,4,5,6,7,8,9,10],x_0:8,x_1:[2,3],x_2:[2,3],x_i:8,x_nonneg:5,xa:3,xai:3,xeq:[2,3],xgt:2,xlt:2,xltz:2,xmem:3,xnt:3,xnu:3,xpo:3,xs:[2,3],xstu:3,xsu:3,xt:3,xtu:3,xu:3,xy:[2,5],y:[0,1,2,3,4,5,6,7,8,9,10],y_nonneg:5,yball:8,yeq:2,yet:[2,3,4,5,6,8],yield:[1,2,3,4,5,8],ylim:8,ylt:2,you:[0,1,2,3,4,5,6,7,8,9,10],your:[0,1,2,3,5,6,7,8],yourself:[2,5],ypo:3,z:[0,1,2,5,6,7,8,9,10],z_nonneg:5,zermelo:2,zero:[2,3,4,5,6,7,8,9,10],zero_add:[1,4,5,6],zero_def:5,zero_dvd_iff:4,zero_im:5,zero_l:[4,5],zero_lt_on:[2,4],zero_lt_two:5,zero_mem:7,zero_mul:[1,4,5,6],zero_r:5,zero_smul:6,zf:2,zlty:2,zmod:7,zsmul:6,zulip:[0,4]},titles:["<span 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>Groups and Rings","<span class=\"section-number\">9. </span>Topology","<span class=\"section-number\">10. </span>Differential Calculus","<span class=\"section-number\">11. </span>Integration and Measure Theory","Index","Mathematics in Lean"],titleterms:{"function":[3,8],"schr\u00f6der":3,The:[2,3],about:1,action:7,algebra:[1,5,7],appli:1,asymptot:9,ball:8,basic:[1,6],bernstein:3,build:5,calcul:1,calculu:9,close:8,compact:8,comparison:9,complet:8,concret:7,conjunct:2,continu:[8,9],converg:[2,8],countabl:8,defin:5,differenti:9,disjunct:2,elementari:[4,9,10],exampl:1,existenti:2,fact:1,filter:8,fundament:8,gaussian:5,get:0,group:7,hierarchi:6,ideal:7,ident:1,iff:2,implic:2,index:11,induct:4,infinit:4,integ:5,integr:10,introduct:0,irrat:4,lean:12,lemma:1,linear:9,logic:2,mani:4,map:9,mathemat:12,measur:10,metric:8,monoid:7,more:1,morphism:[6,7],negat:2,norm:9,number:4,object:6,open:8,overview:0,polynomi:7,prime:4,prove:1,quantifi:2,quotient:7,recurs:4,ring:7,root:4,rw:1,separ:8,sequenc:2,set:[3,8],space:[8,9],start:0,structur:[1,5],sub:6,subgroup:7,subr:7,theorem:[1,3],theori:[4,10],topolog:8,uniformli:8,unit:7,univers:2,us:1}})
• lake-manifest.json
  • @@ -1,52 +1,59 @@
    - {"version": 6, - "packagesDir": "lake-packages", + {"version": 7, + "packagesDir": ".lake/packages", "packages": - [{"git": - {"url": "https://github.com/leanprover-community/mathlib4", - "subDir?": null, - "rev": "5c9a2858ec8178550107ce072e8d1119429752df", - "opts": {}, - "name": "mathlib", - "inputRev?": "master", - "inherited": false}}, - {"git": - {"url": "https://github.com/leanprover/std4", - "subDir?": null, - "rev": "b35ae7244d3372031b56646689117a3e4edf19b7", - "opts": {}, - "name": "std", - "inputRev?": "main", - "inherited": true}}, - {"git": - {"url": "https://github.com/leanprover-community/quote4", - "subDir?": null, - "rev": "a387c0eb611857e2460cf97a8e861c944286e6b2", - "opts": {}, - "name": "Qq", - "inputRev?": "master", - "inherited": true}}, - {"git": - {"url": "https://github.com/leanprover-community/aesop", - "subDir?": null, - "rev": "9dc4a1097a690216eaa7cf2d2290efd447e60d7a", - "opts": {}, - "name": "aesop", - "inputRev?": "master", - "inherited": true}}, - {"git": - {"url": "https://github.com/leanprover/lean4-cli", - "subDir?": null, - "rev": "39229f3630d734af7d9cfb5937ddc6b41d3aa6aa", - "opts": {}, - "name": "Cli", - "inputRev?": "nightly", - "inherited": true}}, - {"git": - {"url": "https://github.com/leanprover-community/ProofWidgets4", - "subDir?": null, - "rev": "27715d1daf32b9657dc38cd52172d77b19bde4ba", - "opts": {}, - "name": "proofwidgets", - "inputRev?": "v0.0.18", - "inherited": true}}], - "name": "mil"} + [{"url": "https://github.com/leanprover/std4", + "type": "git", + "subDir": null, + "rev": "9e37a01f8590f81ace095b56710db694b5bf8ca0", + "name": "std", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.lean"}, + {"url": "https://github.com/leanprover-community/quote4", + "type": "git", + "subDir": null, + "rev": "ccba5d35d07a448fab14c0e391c8105df6e2564c", + "name": "Qq", + "manifestFile": "lake-manifest.json", + "inputRev": "master", + "inherited": true, + "configFile": "lakefile.lean"}, + {"url": "https://github.com/leanprover-community/aesop", + "type": "git", + "subDir": null, + "rev": "3141402ba5a5f0372d2378fd75a481bc79a74ecf", + "name": "aesop", + "manifestFile": "lake-manifest.json", + "inputRev": "master", + "inherited": true, + "configFile": "lakefile.lean"}, + {"url": "https://github.com/leanprover-community/ProofWidgets4", + "type": "git", + "subDir": null, + "rev": "909febc72b4f64628f8d35cd0554f8a90b6e0749", + "name": "proofwidgets", + "manifestFile": "lake-manifest.json", + "inputRev": "v0.0.23", + "inherited": true, + "configFile": "lakefile.lean"}, + {"url": "https://github.com/leanprover/lean4-cli", + "type": "git", + "subDir": null, + "rev": "a751d21d4b68c999accb6fc5d960538af26ad5ec", + "name": "Cli", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.lean"}, + {"url": "https://github.com/leanprover-community/mathlib4", + "type": "git", + "subDir": null, + "rev": "19096ec3fc6f290dc088f7f3ffd6318d4a0bd93d", + "name": "mathlib", + "manifestFile": "lake-manifest.json", + "inputRev": "master", + "inherited": false, + "configFile": "lakefile.lean"}], + "name": "mil", + "lakeDir": ".lake"}
• lakefile.lean
  • @@ -1,20 +1,14 @@
    import Lake open Lake DSL - def moreServerArgs := #[ - "-Dpp.unicode.fun=true", -- pretty-prints `fun a ↦ b` - "-DautoImplicit=false", - "-DrelaxedAutoImplicit=false" - ] - - -- These settings only apply during `lake build`, but not in VSCode editor. - def moreLeanArgs := moreServerArgs - package mil where - moreServerArgs := moreServerArgs + leanOptions := #[ + ⟨`pp.unicode.fun, true⟩, -- pretty-prints `fun a ↦ b` + ⟨`autoImplicit, false⟩, + ⟨`relaxedAutoImplicit, false⟩] @[default_target] lean_lib MIL where - moreLeanArgs := moreLeanArgs require mathlib from git "https://github.com/leanprover-community/mathlib4"@"master" +
• lean-toolchain
  • @@ -1,1 +1,1 @@
    - leanprover/lean4:v4.2.0-rc4 + leanprover/lean4:v4.4.0-rc1
• mathematics_in_lean.pdf