rename [New/Only/Disabled][Tactic/Lemma/Definition]

2023-03-08 09:30:01 +01:00
parent 01199c3793
commit 93d05c9703
91 changed files with 155 additions and 155 deletions
@@ -201,19 +201,19 @@ elab "TacticDoc" name:ident content:str : command =>
    content := content.getString })

 /-- Declare tactics that are introduced by this level. -/
-elab "NewTactics" args:ident* : command => do
+elab "NewTactic" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Tactic name
  modifyCurLevel fun level => pure {level with tactics := {level.tactics with new := names}}

 /-- Declare tactics that are temporarily disabled in this level -/
-elab "DisabledTactics" args:ident* : command => do
+elab "DisabledTactic" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Tactic name
  modifyCurLevel fun level => pure {level with tactics := {level.tactics with disabled := names}}

 /-- Temporarily disable all tactics except the ones declared here -/
-elab "OnlyTactics" args:ident* : command => do
+elab "OnlyTactic" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Tactic name
  modifyCurLevel fun level => pure {level with tactics := {level.tactics with only := names}}
@@ -231,19 +231,19 @@ elab "DefinitionDoc" name:ident content:str : command =>
    content := content.getString })

 /-- Declare definitions that are introduced by this level. -/
-elab "NewDefinitions" args:ident* : command => do
+elab "NewDefinition" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Definition name
  modifyCurLevel fun level => pure {level with definitions := {level.definitions with new := names}}

 /-- Declare definitions that are temporarily disabled in this level -/
-elab "DisabledDefinitions" args:ident* : command => do
+elab "DisabledDefinition" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Definition name
  modifyCurLevel fun level => pure {level with definitions := {level.definitions with disabled := names}}

 /-- Temporarily disable all definitions except the ones declared here -/
-elab "OnlyDefinitions" args:ident* : command => do
+elab "OnlyDefinition" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Definition name
  modifyCurLevel fun level => pure {level with definitions := {level.definitions with only := names}}
@@ -264,19 +264,19 @@ elab "LemmaDoc" name:ident "as" userName:ident "in" category:str content:str : c
    content := content.getString })

 /-- Declare lemmas that are introduced by this level. -/
-elab "NewLemmas" args:ident* : command => do
+elab "NewLemma" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Lemma name
  modifyCurLevel fun level => pure {level with lemmas := {level.lemmas with new := names}}

 /-- Declare lemmas that are temporarily disabled in this level -/
-elab "DisabledLemmas" args:ident* : command => do
+elab "DisabledLemma" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Lemma name
  modifyCurLevel fun level => pure {level with lemmas := {level.lemmas with disabled := names}}

 /-- Temporarily disable all lemmas except the ones declared here -/
-elab "OnlyLemmas" args:ident* : command => do
+elab "OnlyLemma" args:ident* : command => do
  let names := args.map (·.getId)
  for name in names do checkInventoryDoc .Lemma name
  modifyCurLevel fun level => pure {level with lemmas := {level.lemmas with only := names}}
@@ -63,8 +63,8 @@ have k : ¬ B

 Conclusion ""

-NewTactics «have»
-DisabledTactics «suffices»
+NewTactic «have»
+DisabledTactic «suffices»

-NewDefinitions Even Odd
-NewLemmas not_even not_odd
+NewDefinition Even Odd
+NewLemma not_even not_odd
@@ -60,7 +60,7 @@ Hint (A : Prop) (B : Prop) (h : A → ¬ B) (k : A) (f : B) : False =>

 Conclusion ""

-NewTactics «suffices»
-DisabledTactics «have»
-NewDefinitions Even Odd
-NewLemmas not_even not_odd
+NewTactic «suffices»
+DisabledTactic «have»
+NewDefinition Even Odd
+NewLemma not_even not_odd
@@ -52,4 +52,4 @@ HiddenHint (A : Prop) (B : Prop) (h : A → B) (b : ¬ B) (a : A) : False =>

 Conclusion ""

-NewTactics by_contra contradiction apply assumption
+NewTactic by_contra contradiction apply assumption
@@ -46,4 +46,4 @@ HiddenHint (A : Prop) (B : Prop) : A → B ↔ (¬ B → ¬ A) =>

 Conclusion ""

-NewTactics contradiction constructor intro by_contra apply assumption
+NewTactic contradiction constructor intro by_contra apply assumption
@@ -61,6 +61,6 @@ Hint (n : ℕ) : Even n → ¬Odd (n ^ 2) =>
 Hint (n : ℕ) : Even n → Even (n ^ 2) =>
 "Diese Aussage hast du bereits als Lemma bewiesen, schau mal in der Bibliothek."

-NewTactics contrapose rw apply
-NewDefinitions Even Odd
-NewLemmas not_even not_odd even_square
+NewTactic contrapose rw apply
+NewDefinition Even Odd
+NewLemma not_even not_odd even_square
@@ -71,6 +71,6 @@ HiddenHint (n: ℕ) (h : Odd (n ^ 2)) (g : Even n) : Even (n ^ 2) =>
 "Probiers mit `apply ...`"


-NewTactics contradiction by_contra rw apply assumption -- TODO: suffices, have
-NewDefinitions Even Odd
-NewLemmas not_odd not_even even_square
+NewTactic contradiction by_contra rw apply assumption -- TODO: suffices, have
+NewDefinition Even Odd
+NewLemma not_odd not_even even_square
@@ -58,8 +58,8 @@ show that $f(x) = x^2 + 2x + 1$.
  unfold f
  ring

-NewTactics «let»
-OnlyTactics «let» intro unfold ring
+NewTactic «let»
+OnlyTactic «let» intro unfold ring

 HiddenHint : ∀ x, f x = x ^ 2 + 2 * x + 1 =>
 "Fang zuerst wie immer mit `intro x` an."
@@ -19,4 +19,4 @@ Statement
    (U T V : Type _) (f : U → V) (g : V → T) (x : U) : (g ∘ f) x = g (f x)  := by
  simp only [Function.comp_apply]

-NewLemmas Function.comp_apply
+NewLemma Function.comp_apply
@@ -57,9 +57,9 @@ Statement ""
  unfold f
  ring

-NewTactics funext by_cases simp_rw linarith
+NewTactic funext by_cases simp_rw linarith

-NewLemmas not_le if_pos if_neg
+NewLemma not_le if_pos if_neg


 Hint : f ∘ g = g ∘ f =>
@@ -29,8 +29,8 @@ Statement "" : Injective (fun (n : ℤ) ↦ n^3 + (n + 3)) := by
  intro a b
  simp

-NewDefinitions Injective
-NewLemmas StrictMono.injective StrictMono.add Odd.strictMono_pow
+NewDefinition Injective
+NewLemma StrictMono.injective StrictMono.add Odd.strictMono_pow


 Hint : Injective fun (n : ℤ) => n ^ 3 + (n + 3) =>
@@ -22,7 +22,7 @@ Statement "" : Injective (fun (n : ℤ) ↦ n + 3) := by
  intro a b
  simp

-NewDefinitions Injective
+NewDefinition Injective

 Hint : Injective (fun (n : ℤ) ↦ n + 3) =>
 "**Robo**: `Injective` ist als `∀ \{a b : U}, f a = f b → a = b`
@@ -37,4 +37,4 @@ HiddenHint (A : Prop) (B : Prop) (hb : B) : A → (A ∧ B) =>
 Hint (A : Prop) (B : Prop) (ha : A) (hb : B) : (A ∧ B) =>
 "Jetzt kannst du die Taktiken aus dem letzten Kapitel verwenden."

-NewTactics intro constructor assumption
+NewTactic intro constructor assumption
@@ -39,4 +39,4 @@ dass $B$ wahr ist."
 HiddenHint (A : Prop) (B : Prop) (ha : A) (h : A → B): B =>
 "Mit `revert ha` kann man die Annahme `ha` als Implikationsprämisse vorne ans Goal anhängen."

-NewTactics revert assumption
+NewTactic revert assumption
@@ -32,7 +32,7 @@ HiddenHint (A : Prop) (B : Prop) (hA : A) (g : A → B) : A =>
 "Nachdem du die Implikation `A → B` angewendet hast, musst du nur noch $A$ zeigen,
 dafür hast du bereits einen Beweis in den Annahmen."

-NewTactics apply assumption
+NewTactic apply assumption

 -- Katex notes
 -- `\\(    \\)` or `$   $` for inline
@@ -32,4 +32,4 @@ HiddenHint (A : Prop) (B : Prop) (C : Prop) (hA : A) (f : A → B) (g : B → C)
 "Du willst $C$ beweisen. Suche also nach einer Implikation $\\ldots \\Rightarrow C$ und wende
 diese mit `apply` an."

-NewTactics intro apply assumption revert
+NewTactic intro apply assumption revert
@@ -48,6 +48,6 @@ Hint (A : Prop) (B : Prop) (C : Prop) (D : Prop) (E : Prop) (F : Prop)
    (i : D → E) (k : E → F) (m : C → F) : D =>
 "Sackgasse. Probier doch einen anderen Weg."

-NewTactics apply assumption revert intro
+NewTactic apply assumption revert intro

 -- https://www.jmilne.org/not/Mamscd.pdf
@@ -38,6 +38,6 @@ aus mehreren Einzelteilen besteht: `⟨A → B, B → A⟩`. Man sagt also Lean,
 ob das Goal aus solchen Einzelteilen \"konstruiert\" werden kann.
 "

-NewTactics constructor assumption
+NewTactic constructor assumption

 -- TODO : `case mpr =>` ist mathematisch noch sinnvoll.
@@ -71,4 +71,4 @@ Hint (A : Prop) (B : Prop) (C : Prop) (D : Prop) (h₁ : C ↔ D) (h₂ : D ↔
 "Das ist nicht der optimale Weg..."


-NewTactics rw assumption
+NewTactic rw assumption
@@ -41,4 +41,4 @@ Hint (A : Prop) (B : Prop) (C : Prop) (h : A ↔ B) (g : B → C) (hA : A) : B =

 Conclusion "Im nächsten Level findest du die zweite Option."

-NewTactics apply assumption
+NewTactic apply assumption
@@ -36,7 +36,7 @@ Conclusion
 "
 "

-NewTactics intro apply rcases assumption
+NewTactic intro apply rcases assumption

 -- -- TODO: The new `cases` works differntly. There is also `cases'`
 -- example (A B : Prop) : (A ↔ B) → (A → B) := by
@@ -50,6 +50,6 @@ Conclusion
 "
 "

-NewTactics apply left right assumption
+NewTactic apply left right assumption

-NewLemmas not_or_of_imp
+NewLemma not_or_of_imp
@@ -34,6 +34,6 @@ Conclusion
 `rw` hat automatisch `rfl` ausgeführt und dadurch den Beweis beendet.
 "

-NewTactics rw
+NewTactic rw

-NewLemmas not_not not_or_of_imp
+NewLemma not_not not_or_of_imp
@@ -76,6 +76,6 @@ HiddenHint (A : Prop) (B: Prop) (h : ¬ A ∨ B) (ha : A) : B =>
 HiddenHint (A : Prop) (B: Prop) (ha : A) (ha' : ¬A) : B =>
 "Findest du einen Widerspruch?"

-NewTactics rfl assumption trivial left right constructor rcases
+NewTactic rfl assumption trivial left right constructor rcases

-NewLemmas not_not not_or_of_imp
+NewLemma not_not not_or_of_imp
@@ -24,7 +24,7 @@ Statement
  rw [Nat.pow_succ, Nat.mul_succ, add_assoc, h, mul_comm, ←mul_add]
  simp

--NewLemmas Nat.pow_succ, Nat.mul_succ, add_assoc, mul_comm, ←mul_add
+--NewLemma Nat.pow_succ, Nat.mul_succ, add_assoc, mul_comm, ←mul_add

 -- example (n : ℕ) : Even (n^2 + n) := by
 --   induction n
@@ -34,8 +34,8 @@ Statement Nat.pos_iff_ne_zero
  intro
  apply Nat.succ_pos

-NewTactics simp
-NewLemmas Nat.succ_pos
+NewTactic simp
+NewLemma Nat.succ_pos

 Hint : 0 < Nat.zero ↔ Nat.zero ≠ 0 =>
 "Den Induktionsanfang kannst du oft mit `simp` lösen."
@@ -18,6 +18,6 @@ Statement
    (n : ℕ) (h : 2 ≤ n) : n ≠ 0 := by
  linarith

-NewTactics linarith
+NewTactic linarith

-NewLemmas Nat.pos_iff_ne_zero
+NewLemma Nat.pos_iff_ne_zero
@@ -38,4 +38,4 @@ Hint (P : ℕ → Prop) (m : ℕ) (hi : P m) : P (Nat.succ m) =>

 In diesem Beispiel kannst du `apply` benützen."

-NewTactics induction
+NewTactic induction
@@ -43,9 +43,9 @@ Statement
  rw [Fin.sum_univ_castSucc (n := m + 1)]
  rfl

-OnlyTactics rw rfl
+OnlyTactic rw rfl

-NewLemmas Fin.sum_univ_castSucc
+NewLemma Fin.sum_univ_castSucc

 HiddenHint (m : ℕ) :
  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i =>
@@ -49,9 +49,9 @@ Statement
  rw [Fin.sum_univ_castSucc (n := m + 1)]
  rfl

-OnlyTactics rw rfl
+OnlyTactic rw rfl

-NewLemmas Fin.sum_univ_castSucc
+NewLemma Fin.sum_univ_castSucc

 Hint (m : ℕ) :
  ∑ i : Fin (m + 1), (i : ℕ) + (m + 1) = ∑ i : Fin (Nat.succ m + 1), ↑i =>
@@ -67,4 +67,4 @@ Hint (A : Prop) (B : Prop) (C : Prop) (h : A ∧ B) : C ∧ A =>
 Hint (A : Prop) (B : Prop) (C : Prop) (h : A → C) : C ∧ A =>
 "Ein UND im Goal kann mit `constructor` aufgeteilt werden."

-NewTactics left right assumption constructor rcases
+NewTactic left right assumption constructor rcases
@@ -20,4 +20,4 @@ Conclusion
 "
 "

-NewTactics ring
+NewTactic ring
@@ -20,4 +20,4 @@ Conclusion
 "
 "

-NewTactics ring
+NewTactic ring
@@ -58,4 +58,4 @@ Hint (n : ℕ) (hn : odd n) (h : ∀ (x : ℕ), (odd x) → even (x + 1)) : even
 "`∀ (x : ℕ), (odd x) → even (x + 1)` ist eigentlich das gleiche wie
 `(x : ℕ) → `"

-NewTactics ring intro unfold
+NewTactic ring intro unfold
@@ -22,4 +22,4 @@ Statement : ∃ (f : ℕ → ℕ), ∀ (x : ℕ), f x = 0 := by

 Conclusion ""

-NewTactics use simp
+NewTactic use simp
@@ -72,4 +72,4 @@ Statement
  simp <;>
  ring

-NewTactics fin_cases funext
+NewTactic fin_cases funext
@@ -40,4 +40,4 @@ Statement
  --   fin_cases i;
  --   simp,

--NewLemmas top_le_span_range_iff_forall_exists_fun le_top
+--NewLemma top_le_span_range_iff_forall_exists_fun le_top
@@ -39,6 +39,6 @@ Ring zu lösen, funktioniert aber auch auf `ℕ`, auch wenn dieses kein Ring ist
 (erst `ℤ` ist ein Ring).
 "

-NewTactics ring
+NewTactic ring

 #eval 4 / 6
@@ -67,4 +67,4 @@ Hint (a : ℕ) (b : ℕ) (c : ℕ) (d : ℕ) (h₁ : c = d) (h₂ : d = b) (h₃

 Conclusion "Übrigens, mit `rw [h₁, ←h₂]` könnte man mehrere `rw` zusammenfassen."

-NewTactics assumption rw
+NewTactic assumption rw
@@ -37,4 +37,4 @@ Hint (a : ℕ) (b : ℕ) (h : a = b) (g : a + a ^ 2 = b + 1) : a + a ^ 2 = a + 1
 Conclusion "Übrigens, mit `rw [h] at *` kann man im weiteren `h` in **allen** Annahmen und
 dem Goal umschreiben."

-NewTactics assumption rw
+NewTactic assumption rw
@@ -30,4 +30,4 @@ Hint (y : ℕ) : (2 * y + 1) ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y =>

 Conclusion ""

-NewTactics ring rw
+NewTactic ring rw
@@ -28,4 +28,4 @@ Conclusion
 aufzurufen, deshalb brauchst du das nur noch selten.
 "

-NewTactics rfl
+NewTactic rfl
@@ -67,5 +67,5 @@ Hint (n : ℕ) (x : ℕ) (hx : n = x + x) : n ^ 2 = 2 * x ^ 2 + 2 * x ^ 2 =>
 Hint (n : ℕ) (x : ℕ) (hx : n = x + x) : (x + x) ^ 2 = 2 * x ^ 2 + 2 * x ^ 2 =>
 "Die Taktik `ring` löst solche Gleichungen."

-NewTactics unfold rcases use rw ring
-NewDefinitions Even Odd
+NewTactic unfold rcases use rw ring
+NewDefinition Even Odd
@@ -50,4 +50,4 @@ Hint (n : ℕ) (hn : Odd n) (h : ∀ (x : ℕ), (Odd x) → Even (x + 1)) : Even
 Conclusion "Für-alle-Statements, Implikationen und Lemmas/Theoreme verhalten sich alle
 praktisch gleich. Mehr dazu später."

-NewTactics ring intro unfold
+NewTactic ring intro unfold
@@ -62,6 +62,6 @@ Hint (n : ℕ) : n + n = 2 * n => "Recap: `ring` löst Gleichungen in `ℕ`."

 Conclusion ""

-NewTactics push_neg intro use rw unfold ring
-NewDefinitions Even Odd
-NewLemmas not_even not_odd not_exists not_forall
+NewTactic push_neg intro use rw unfold ring
+NewDefinition Even Odd
+NewLemma not_even not_odd not_exists not_forall
@@ -50,6 +50,6 @@ Statement

 Conclusion ""

-NewTactics push_neg intro use rw unfold ring
-NewDefinitions Even Odd
-NewLemmas not_even not_odd not_exists not_forall
+NewTactic push_neg intro use rw unfold ring
+NewDefinition Even Odd
+NewLemma not_even not_odd not_exists not_forall
@@ -43,4 +43,4 @@ Statement
  rcases h with ⟨_, h₂⟩
  assumption

-NewLemmas Nat.prime_def_lt''
+NewLemma Nat.prime_def_lt''
@@ -47,4 +47,4 @@ Aber glaubt bloß nicht, dass Ihr damit auf *diesem* Planeten viel weiterkommt!
 Meine Untertanen verstehen `tauto` nicht.  Da müsst Ihr Euch schon etwas mehr anstrengen.
 "

-NewTactics tauto
+NewTactic tauto
@@ -31,5 +31,5 @@ Conclusion
 **Untertan** Ah, richtig. Ja, Sie haben ja so recht.  Das vergesse ich immer.  Rfl, rfl, rfl …
 "

-NewTactics rfl
-DisabledTactics tauto
+NewTactic rfl
+DisabledTactic tauto
@@ -41,5 +41,5 @@ Conclusion
 zerbrochen habe!
 "

-NewTactics assumption
-DisabledTactics tauto
+NewTactic assumption
+DisabledTactic tauto
@@ -34,5 +34,5 @@ Conclusion
 **Untertan** Das ging ja schnell. Super! Vielen Dank.
 "

-NewTactics assumption
-DisabledTactics tauto
+NewTactic assumption
+DisabledTactic tauto
@@ -35,5 +35,5 @@ Wie in einer Mathe-Vorlesung?
 Das funktioniert nur in einer Handvoll Situationen.
 "

-NewTactics trivial
-DisabledTactics tauto
+NewTactic trivial
+DisabledTactic tauto
@@ -33,5 +33,5 @@ Conclusion
 Die Schwester lacht und eilt ihrem Bruder hinterher.
 "

-NewTactics trivial
-DisabledTactics tauto
+NewTactic trivial
+DisabledTactic tauto
@@ -45,5 +45,5 @@ Conclusion
 wir haben eine `contradiction` in unserem Annahmen, also folgt jede beliebige Aussage.
 "

-NewTactics contradiction
-DisabledTactics tauto
+NewTactic contradiction
+DisabledTactic tauto
@@ -39,5 +39,5 @@ Und gleich 38, und gleich 39, …
 **Du** Ok, ok, verstehe.
 "

-NewTactics contradiction
-DisabledTactics tauto
+NewTactic contradiction
+DisabledTactic tauto
@@ -33,5 +33,5 @@ worin der Widerspruch besteht:  Die Annahme `n ≠ 10` ist genau die Negation vo
 Man muss `≠` immer als `¬(· = ·)` lesen.
 "

-NewTactics contradiction
-DisabledTactics tauto
+NewTactic contradiction
+DisabledTactic tauto
@@ -54,5 +54,5 @@ Ihm scheinen diese Fragen inzwischen Spaß zu machen.
 Oder ist der nur gemalt?  Probier mal!
 "

-NewTactics constructor
-DisabledTactics tauto
+NewTactic constructor
+DisabledTactic tauto
@@ -47,5 +47,5 @@ Conclusion
 `rcases h with ⟨h₁, ⟨h₂ , h₃⟩⟩`.
 "

-NewTactics rcases
-DisabledTactics tauto
+NewTactic rcases
+DisabledTactic tauto
@@ -44,5 +44,5 @@ Conclusion
 Auch dieser Formalosoph zieht zufrieden von dannen.
 "

-NewTactics left right assumption
-DisabledTactics tauto
+NewTactic left right assumption
+DisabledTactic tauto
@@ -125,5 +125,5 @@ Die Worte, die Du aktiv gebrauchen musst, heißen zusammengefasst `Taktiken`.  H
 "


-NewTactics assumption rcases
-DisabledTactics tauto
+NewTactic assumption rcases
+DisabledTactic tauto
@@ -74,5 +74,5 @@ Conclusion
 Königin *Logisinde* ist in der Zwischenzeit eingeschlafen, und ihr stehlt euch heimlich davon.
 "

-NewTactics left right assumption constructor rcases rfl contradiction trivial
-DisabledTactics tauto
+NewTactic left right assumption constructor rcases rfl contradiction trivial
+DisabledTactic tauto
@@ -39,4 +39,4 @@ Statement mem_univ
  trivial
  -- tauto

-NewTactics tauto trivial
+NewTactic tauto trivial
@@ -39,7 +39,7 @@ Statement subset_empty_iff
  intro h hA
  apply mem_univ -- or `trivial`.

-NewTactics intro trivial apply
+NewTactic intro trivial apply
 -- blocked: tauto simp

 end MySet
@@ -54,8 +54,8 @@ Statement subset_empty_iff
  rcases a with ⟨h₁, h₂⟩
  assumption

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset

 end MySet
@@ -45,8 +45,8 @@ Statement eq_empty_iff_forall_not_mem
  rw [←subset_empty_iff]
  rfl -- This is quite a miracle :)

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset

 end MySet
@@ -30,6 +30,6 @@ Statement nonempty_iff_ne_empty
  push_neg
  rfl

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -26,6 +26,6 @@ Statement
 "" (A B : Set ℕ) : (A ∪ ∅) ∩ B = A ∩ (univ ∩ B) := by
  simp

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -30,6 +30,6 @@ Statement
  rw [←union_diff_distrib]
  rw [univ_union]

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -30,6 +30,6 @@ Statement
  rw [←not_mem_compl_iff]
  exact h4

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -22,7 +22,7 @@ man die de-Morganschen Regeln einfach selber beweisen könnten.


 Die meisten Aufgaben über Mengen sind eine Kombination von `rw` und `simp_rw` verschiedenster
-NewLemmas in `import Mathlib.Data.Set`.
+NewLemma in `import Mathlib.Data.Set`.

 Die Taktik `simp_rw` funktioniert ähnlich wie `rw`, aber sie versucht jedes Lemma so oft
 wie möglich anzuwenden. Wir kennen also 4 etwas verwandte Optionen um Lemmas und Theoreme zu
@@ -52,7 +52,7 @@ Statement
  rw [diff_eq_compl_inter]
  rw [inter_comm]

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

 -- TODOs
 -- Lemmas compl_union compl_inter mem_compl_iff
@@ -33,6 +33,6 @@ Statement
  rw [Set.mem_diff]
  exact hx

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -32,6 +32,6 @@ Statement
    ({4, 9} : Set ℕ) = Set.insert 4 {9} := by
  rfl

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -35,5 +35,5 @@ Statement
  simp_rw [mem_insert_iff, mem_singleton_iff] at *
  tauto

-NewTactics simp_rw intro tauto rw
+NewTactic simp_rw intro tauto rw
 --Lemmas Subset.antisymm_iff empty_subset
@@ -32,6 +32,6 @@ Statement
  use 1
  ring

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -37,6 +37,6 @@ Statement
  assumption


-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -36,6 +36,6 @@ Statement
  ring


-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -34,6 +34,6 @@ Statement
  ring


-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -28,6 +28,6 @@ Statement
    { x ∈ (S : Set ℤ) | 0 ≤ x} ⊆ S := by
  library_search

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -23,6 +23,6 @@ Statement
  use 1
  ring

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -22,6 +22,6 @@ open Set
 Statement
 "" : True := sorry

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -23,6 +23,6 @@ Statement
  use 1
  ring

-NewTactics constructor intro rw assumption rcases simp tauto trivial
+NewTactic constructor intro rw assumption rcases simp tauto trivial

-NewLemmas Subset.antisymm_iff empty_subset
+NewLemma Subset.antisymm_iff empty_subset
@@ -54,7 +54,7 @@ Statement
  rw [←Set.union_diff_distrib]
  rw [Set.univ_union]

-NewTactics rw
+NewTactic rw

 example : 4 ∈ (univ : Set ℕ) := by
  trivial
@@ -35,4 +35,4 @@ lemma asdf (a b c d : ℕ) (h₁ : c = d) (h₂ : a = b) (h₃ : a = d) : b = c

 Conclusion ""

-NewTactics assumption
+NewTactic assumption
@@ -44,4 +44,4 @@ Statement
    (n : ℕ) : (∑ i : Fin n, (0 + 0)) = 0 := by
  simp

-NewTactics simp
+NewTactic simp
@@ -34,7 +34,7 @@ Statement
  simp
  ring

-NewLemmas Finset.sum_add_distrib add_comm
+NewLemma Finset.sum_add_distrib add_comm

 Hint (n : ℕ) : ∑ x : Fin n, ↑x + ∑ x : Fin n, 1 = n + ∑ i : Fin n, ↑i =>
 "Die zweite Summe `∑ x : Fin n, 1` kann `simp` zu `n` vereinfacht werden."
@@ -52,8 +52,8 @@ Statement arithmetic_sum
  rw [Nat.succ_eq_add_one]
  ring

-NewTactics induction
-NewLemmas Fin.sum_univ_castSucc Nat.succ_eq_add_one mul_add add_mul
+NewTactic induction
+NewLemma Fin.sum_univ_castSucc Nat.succ_eq_add_one mul_add add_mul

 Hint (n : ℕ) : 2 * (∑ i : Fin (n + 1), ↑i) = n * (n + 1) =>
 "Als Erinnerung, einen Induktionsbeweis startet man mit `induction n`."
@@ -33,4 +33,4 @@ $\\sum_{i=0}^n\\sum_{j=0}^m  2^i (1 + j) = \\sum_{j=0}^m\\sum_{i=0}^n  2^i (1 +
    ∑ j : Fin m, ∑ i : Fin n, ( 2^i * (1 + j) : ℕ) := by
  rw [Finset.sum_comm]

-NewLemmas Finset.sum_comm
+NewLemma Finset.sum_comm
@@ -57,7 +57,7 @@ Statement
  rw [arithmetic_sum]
  ring

-NewLemmas arithmetic_sum add_pow_two
+NewLemma arithmetic_sum add_pow_two

 HiddenHint (m : ℕ) : ∑ i : Fin (m + 1), (i : ℕ) ^ 3 = (∑ i : Fin (m + 1), ↑i) ^ 2 =>
 "Führe auch hier einen Induktionsbeweis."
@@ -37,4 +37,4 @@ example (n : ℕ) (h : 5 ≤ n) : n^2 < 2 ^ n
  sorry
 | n + 5  => by sorry

-NewTactics rw simp ring
+NewTactic rw simp ring
@@ -32,4 +32,4 @@ Statement
 --   ring
 --   rw [Nat.succ_eq_one_add]
 --   rw []
-NewTactics rw simp ring
+NewTactic rw simp ring
@@ -46,4 +46,4 @@ Statement
  -- rw [mul_add, hn]
  -- ring

-NewTactics ring
+NewTactic ring