compute which tactics are available in which level

pull/43/head
Alexander Bentkamp 3 years ago
parent 03faa3ffed
commit 76d1a08948

@ -190,16 +190,8 @@ instance : Quote TacticDocEntry `term :=
/-- Declare the list of tactics that will be displayed in the current level.
Expects a space separated list of identifiers that refer to either a tactic doc
entry or a tactic doc set. -/
elab "Tactics" args:ident* : command => do
let env ← getEnv
let docs := tacticDocExt.getState env
let mut tactics : Array TacticDocEntry := #[]
for arg in args do
let name := arg.getId
match docs.find? (·.name = name) with
| some entry => tactics := tactics.push entry
| none => throwError "Tactic doc {name} wasn't found."
modifyCurLevel fun level => pure {level with tactics := tactics}
elab "NewTactics" args:ident* : command => do
modifyCurLevel fun level => pure {level with newTactics := args.map (·.getId)}
/-! ## Lemmas -/
@ -219,11 +211,11 @@ Expect an identifier used as the set name then `:=` and a
space separated list of identifiers. -/
elab "LemmaSet" name:ident ":" title:str ":=" args:ident* : command => do
let docs := lemmaDocExt.getState (← getEnv)
let mut entries : Array LemmaDocEntry := #[]
let mut entries : Array Name := #[]
for arg in args do
let name := arg.getId
match docs.find? (·.userName = name) with
| some doc => entries := entries.push doc
| some doc => entries := entries.push name
| none => throwError "Lemma doc {name} wasn't found."
modifyEnv (lemmaSetExt.addEntry · {
name := name.getId,
@ -236,16 +228,60 @@ instance : Quote LemmaDocEntry `term :=
/-- Declare the list of lemmas that will be displayed in the current level.
Expects a space separated list of identifiers that refer to either a lemma doc
entry or a lemma doc set. -/
elab "Lemmas" args:ident* : command => do
elab "NewLemmas" args:ident* : command => do
let env ← getEnv
let docs := lemmaDocExt.getState env
let sets := lemmaSetExt.getState env
let mut lemmas : Array LemmaDocEntry := #[]
let mut lemmas : Array Name := #[]
for arg in args do
let name := arg.getId
match docs.find? (·.userName = name) with
| some entry => lemmas := lemmas.push entry
| some entry => lemmas := lemmas.push name
| none => match sets.find? (·.name = name) with
| some entry => lemmas := lemmas ++ entry.lemmas
| none => throwError "Lemma doc or lemma set {name} wasn't found."
modifyCurLevel fun level => pure {level with lemmas := lemmas}
modifyCurLevel fun level => pure {level with newLemmas := lemmas}
/-! ## Make Game -/
def getTacticDoc! (tac : Name) : CommandElabM TacticDocEntry := do
match (tacticDocExt.getState (← getEnv)).find? (·.name = tac) with
| some doc => return doc
| none => throwError "Tactic documentation not found: {tac}"
/-- Make the final Game. This command will precompute various things about the game, such as which
tactics are available in each level etc. -/
elab "MakeGame" : command => do
let game ← getCurGame
-- Check for loops in world graph
if game.worlds.hasLoops then
throwError "World graph has loops!"
-- Compute which tactics are available in which level:
let mut newTacticsInWorld : HashMap Name (HashSet Name) := {}
for (worldId, world) in game.worlds.nodes.toArray do
let mut newTactics : HashSet Name:= {}
for (_, level) in world.levels.toArray do
newTactics := newTactics.insertMany level.newTactics
newTacticsInWorld := newTacticsInWorld.insert worldId newTactics
let mut tacticsInWorld : HashMap Name (HashSet Name) := {}
for (worldId, _) in game.worlds.nodes.toArray do
let mut tactics : HashSet Name:= {}
let predecessors := game.worlds.predecessors worldId
for predWorldId in predecessors do
tactics := tactics.insertMany (newTacticsInWorld.find! predWorldId)
tacticsInWorld := tacticsInWorld.insert worldId tactics
for (worldId, world) in game.worlds.nodes.toArray do
let mut tactics := tacticsInWorld.find! worldId
logInfo m!"{tactics.toArray}"
let levels := world.levels.toArray.insertionSort fun a b => a.1 < b.1
for (levelId, level) in levels do
tactics := tactics.insertMany level.newTactics
modifyLevel ⟨← getCurGameId, worldId, levelId⟩ fun level => do
return {level with tactics := ← tactics.toArray.mapM getTacticDoc!}

@ -1,4 +1,6 @@
import Lean
import GameServer.Graph
/-! # Environment extensions
The game framework stores almost all its game building data in environment extensions
@ -71,7 +73,7 @@ elab "#print_lemma_doc" : command => do
structure LemmaSetEntry where
name : Name
title : String
lemmas : Array LemmaDocEntry
lemmas : Array Name
deriving ToJson, Repr
/-- Environment extension for lemma sets. -/
@ -86,26 +88,8 @@ open Elab Command in
/-- Print all registered lemma sets for debugging purposes. -/
elab "#print_lemma_set" : command => do
for entry in lemmaSetExt.getState (← getEnv) do
dbg_trace "{entry.name} : {entry.lemmas.map LemmaDocEntry.name}"
/-! ## Graph -/
structure Graph (α β : Type) [inst : BEq α] [inst : Hashable α] where
nodes: HashMap α β := {}
edges: Array (α × α) := {}
deriving Inhabited
instance [ToJson β] : ToJson (Graph Name β) := {
toJson := fun graph => Json.mkObj [
("nodes", Json.mkObj (graph.nodes.toList.map fun (a,b) => (a.toString, toJson b))),
("edges", toJson graph.edges)
]
}
instance [inst : BEq α] [inst : Hashable α] : EmptyCollection (Graph α β) := ⟨default⟩
dbg_trace "{entry.name} : {entry.lemmas}"
def Graph.insertNode [inst : BEq α] [inst : Hashable α] (g : Graph α β) (a : α) (b : β) :=
{g with nodes := g.nodes.insert a b}
/-! ## Environment extensions for game specification-/
@ -179,7 +163,21 @@ structure GameLevel where
introduction: String := default
description: String := default
conclusion: String := default
-- new tactics introduces by this level:
newTactics: Array Name := default
-- tactics exceptionally forbidden in this level:
disabledTactics: Array Name := default
-- only these tactics are allowed in this level (ignore if empty):
onlyTactics: Array Name := default
-- tactics in this level (computed by `MakeGame`):
tactics: Array TacticDocEntry := default
-- new lemmas introduces by this level:
newLemmas: Array Name := default
-- lemmas exceptionally forbidden in this level:
disabledLemmas: Array Name := default
-- only these lemmas are allowed in this level (ignore if empty):
onlyLemmas: Array Name := default
-- lemmas in this level (computed by `MakeGame`):
lemmas: Array LemmaDocEntry := default
hints: Array GoalHintEntry := default
goal : TSyntax `Lean.Parser.Command.declSig := default
@ -310,3 +308,15 @@ def modifyCurLevel (fn : GameLevel → m GameLevel) [MonadError m] : m Unit := d
modifyCurWorld fun world => do
let level ← getCurLevel
return {world with levels := world.levels.insert level.index (← fn level)}
def modifyLevel (levelId : LevelId) (fn : GameLevel → m GameLevel) [MonadError m] : m Unit := do
let some game ← getGame? levelId.game
| throwError m!"Game {levelId.game} does not exist"
let some world := (← getCurGame).worlds.nodes.find? levelId.world
| throwError m!"World {levelId.world} does not exist"
let some level := world.levels.find? levelId.level
| throwError m!"Level {levelId.level} does not exist"
let level' ← fn level
let world' := {world with levels := world.levels.insert levelId.level level'}
let game' := {game with worlds := game.worlds.insertNode levelId.world world'}
insertGame levelId.game game'

@ -39,9 +39,12 @@ Conclusion
Path Proposition → Implication → Predicate → Contradiction → LeanStuff
--Path Predicate → Prime
-- Path Predicate → Prime
Path Predicate → Induction → LeanStuff → Function → SetFunction
Path LeanStuff → SetTheory → SetFunction
Path SetTheory → SetTheory2
MakeGame

@ -63,6 +63,6 @@ have k : ¬ B
Conclusion ""
Tactics contradiction rcases haveₓ assumption apply
NewTactics contradiction rcases haveₓ assumption apply
Lemmas Even Odd not_even not_odd
NewLemmas Even Odd not_even not_odd

@ -60,6 +60,6 @@ Hint (A : Prop) (B : Prop) (h : A → ¬ B) (g : A) (f : B) : False =>
Conclusion ""
Tactics contradiction apply assumption rcases sufficesₓ
NewTactics contradiction apply assumption rcases sufficesₓ
Lemmas Even Odd not_even not_odd
NewLemmas Even Odd not_even not_odd

@ -52,4 +52,4 @@ HiddenHint (A : Prop) (B : Prop) (h : A → B) (b : ¬ B) (a : A) : False =>
Conclusion ""
Tactics by_contra sufficesₓ haveₓ contradiction apply assumption
NewTactics by_contra sufficesₓ haveₓ contradiction apply assumption

@ -46,4 +46,4 @@ HiddenHint (A : Prop) (B : Prop) : A → B ↔ (¬ B → ¬ A) =>
Conclusion ""
Tactics contradiction constructor intro by_contra sufficesₓ haveₓ apply assumption
NewTactics contradiction constructor intro by_contra sufficesₓ haveₓ apply assumption

@ -61,5 +61,5 @@ Hint (n : ) : Even n → ¬Odd (n ^ 2) =>
Hint (n : ) : Even n → Even (n ^ 2) =>
"Diese Aussage hast du bereits als Lemma bewiesen, schau mal in der Bibliothek."
Tactics contrapose rw apply
Lemmas Even Odd not_even not_odd even_square
NewTactics contrapose rw apply
NewLemmas Even Odd not_even not_odd even_square

@ -71,6 +71,6 @@ HiddenHint (n: ) (h : Odd (n ^ 2)) (g : Even n) : Even (n ^ 2) =>
"Probiers mit `apply ...`"
Tactics contradiction by_contra rw apply assumption -- TODO: suffices, have
NewTactics contradiction by_contra rw apply assumption -- TODO: suffices, have
Lemmas Odd Even not_odd not_even even_square
NewLemmas Odd Even not_odd not_even even_square

@ -23,4 +23,4 @@ Statement
: True := by
trivial
Tactics rw
NewTactics rw

@ -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."
Tactics intro constructor assumption
NewTactics 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."
Tactics revert assumption
NewTactics 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."
Tactics apply assumption
NewTactics 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."
Tactics intro apply assumption revert
NewTactics 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."
Tactics apply assumption revert intro
NewTactics 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.
"
Tactics constructor assumption
NewTactics 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..."
Tactics rw assumption
NewTactics 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."
Tactics apply assumption
NewTactics apply assumption

@ -36,7 +36,7 @@ Conclusion
"
"
Tactics intro apply rcases assumption
NewTactics 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
"
"
Tactics apply left right assumption
NewTactics apply left right assumption
Lemmas not_or_of_imp
NewLemmas not_or_of_imp

@ -34,6 +34,6 @@ Conclusion
`rw` hat automatisch `rfl` ausgeführt und dadurch den Beweis beendet.
"
Tactics rw
NewTactics rw
Lemmas not_not not_or_of_imp
NewLemmas 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?"
Tactics rfl assumption trivial left right constructor rcases
NewTactics rfl assumption trivial left right constructor rcases
Lemmas not_not not_or_of_imp
NewLemmas not_not not_or_of_imp

@ -43,4 +43,4 @@ Statement
(n : ) : (∑ i : Fin n, (0 + 0)) = 0 := by
simp
Tactics simp
NewTactics simp

@ -34,4 +34,4 @@ Statement
simp
ring
Tactics rw simp ring
NewTactics rw simp ring

@ -43,4 +43,4 @@ Statement
-- rw [mul_add, hn]
-- ring
Tactics ring
NewTactics ring

@ -30,4 +30,4 @@ $\\sum_{i = 0}^n (2n + 1) = n ^ 2$."
--rw [hn]
--ring
Tactics ring
NewTactics ring

@ -44,4 +44,4 @@ Statement
-- rw [mul_add, hn]
-- ring
Tactics ring
NewTactics ring

@ -23,4 +23,4 @@ Statement
simp
sorry
Tactics ring
NewTactics ring

@ -21,4 +21,4 @@ Statement
(n : ) : True := by
sorry
Tactics rw simp ring
NewTactics rw simp ring

@ -21,4 +21,4 @@ Statement
(n : ) : True := by
sorry
Tactics rw simp ring
NewTactics rw simp ring

@ -21,7 +21,7 @@ Statement
(n : ) : True := by
trivial
Tactics simp
NewTactics simp
-- Σ_i Σ_j ... = Σ_j Σ_i ...

@ -29,4 +29,4 @@ Statement
"TODO" : True := by
trivial
Tactics rw
NewTactics rw

@ -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."
Tactics left right assumption constructor rcases
NewTactics left right assumption constructor rcases

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

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

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

@ -22,4 +22,4 @@ Statement : ∃ (f : ), ∀ (x : ), f x = 0 := by
Conclusion ""
Tactics use simp
NewTactics use simp

@ -39,6 +39,6 @@ Ring zu lösen, funktioniert aber auch auf ``, auch wenn dieses kein Ring ist
(erst `` ist ein Ring).
"
Tactics ring
NewTactics ring
#eval 4 / 6

@ -67,4 +67,4 @@ Hint (a : ) (b : ) (c : ) (d : ) (h₁ : c = d) (h₂ : d = b) (h₃
Conclusion "Übrigens, mit `rw [h₁, ←h₂]` könnte man mehrere `rw` zusammenfassen."
Tactics assumption rw
NewTactics assumption rw

@ -37,4 +37,4 @@ Hint (a : ) (b : ) (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."
Tactics assumption rw
NewTactics assumption rw

@ -30,4 +30,4 @@ Hint (y : ) : (2 * y + 1) ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y =>
Conclusion ""
Tactics ring rw
NewTactics ring rw

@ -28,4 +28,4 @@ Conclusion
aufzurufen, deshalb brauchst du das nur noch selten.
"
Tactics rfl
NewTactics rfl

@ -67,5 +67,5 @@ Hint (n : ) (x : ) (hx : n = x + x) : n ^ 2 = 2 * x ^ 2 + 2 * x ^ 2 =>
Hint (n : ) (x : ) (hx : n = x + x) : (x + x) ^ 2 = 2 * x ^ 2 + 2 * x ^ 2 =>
"Die Taktik `ring` löst solche Gleichungen."
Tactics unfold rcases use rw ring
Lemmas Even Odd
NewTactics unfold rcases use rw ring
NewLemmas Even Odd

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

@ -62,6 +62,6 @@ Hint (n : ) : n + n = 2 * n => "Recap: `ring` löst Gleichungen in ``."
Conclusion ""
Tactics push_neg intro use rw unfold ring
NewTactics push_neg intro use rw unfold ring
Lemmas Even Odd not_even not_odd not_exists not_forall
NewLemmas Even Odd not_even not_odd not_exists not_forall

@ -50,6 +50,6 @@ Statement
Conclusion ""
Tactics push_neg intro use rw unfold ring
NewTactics push_neg intro use rw unfold ring
Lemmas Even Odd not_even not_odd not_exists not_forall
NewLemmas Even Odd not_even not_odd not_exists not_forall

@ -34,6 +34,6 @@ Statement
Conclusion ""
Tactics
NewTactics
Lemmas
NewLemmas

@ -48,4 +48,4 @@ HiddenHint (A : Prop) (B : Prop) (C : Prop): ¬((¬B ¬ C) (A → B))
Conclusion ""
Tactics tauto
NewTactics tauto

@ -27,4 +27,4 @@ HiddenHint : 42 = 42 =>
Conclusion "Bravo! PS: `rfl` steht für \"reflexivity\"."
Tactics rfl
NewTactics rfl

@ -32,4 +32,4 @@ HiddenHint (n : ) (h : 1 < n) : 1 < n =>
Conclusion ""
Tactics assumption
NewTactics assumption

@ -27,4 +27,4 @@ HiddenHint (A : Prop) (hA : A) : A =>
Conclusion ""
Tactics assumption
NewTactics assumption

@ -33,4 +33,4 @@ True := by
Conclusion ""
Tactics trivial
NewTactics trivial

@ -21,4 +21,4 @@ Statement
Conclusion ""
Tactics trivial
NewTactics trivial

@ -27,4 +27,4 @@ HiddenHint (A : Prop) (h : False) : A =>
"Wenn man einen Beweis von `False` hat, kann man mit `contradiction` das Goal beweisen,
unabhängig davon, was das Goal ist."
Tactics contradiction
NewTactics contradiction

@ -26,4 +26,4 @@ Conclusion
"
"
Tactics contradiction
NewTactics contradiction

@ -29,4 +29,4 @@ Conclusion
"
"
Tactics contradiction
NewTactics contradiction

@ -32,7 +32,7 @@ HiddenHint (A : Prop) (B : Prop) (hA : A) (hB : B) : A ∧ B =>
HiddenHint (A : Prop) (hA : A) : A =>
"Du hast einen Beweis dafür in den *Annahmen*."
Tactics constructor assumption
NewTactics constructor assumption
-- Statement
-- "Zeige $(A \\land (A \\Rightarrow B)) \\iff (A \\land B)$."

@ -33,7 +33,7 @@ HiddenHint (A : Prop) (B : Prop) (C : Prop) (h : A ∧ (B ∧ C)) : B =>
HiddenHint (A : Prop) (hA : A) : A =>
"Du hast einen Beweis dafür in den *Annahmen*."
Tactics constructor assumption
NewTactics constructor assumption
-- Statement
-- "Zeige $(A \\land (A \\Rightarrow B)) \\iff (A \\land B)$."

@ -30,4 +30,4 @@ HiddenHint (A : Prop) (B : Prop) (hA : A) : A (¬ B) =>
Hint (A : Prop) (B : Prop) (hA : A) : ¬ B =>
"Sackgasse. Probier's nochmals."
Tactics left right assumption
NewTactics left right assumption

@ -44,4 +44,4 @@ HiddenHint (A : Prop) (B : Prop) (h : A (A ∧ B)) : A =>
Hint (A : Prop) (B : Prop) (h : A ∧ B) : A =>
"Jetzt noch das UND in den Annahmen mit `rcases h with ⟨h₁, h₂⟩` zerlegen."
Tactics assumption rcases
NewTactics assumption rcases

@ -122,4 +122,4 @@ HiddenHint (A : Prop) (B : Prop) (C : Prop) (h : B ∧ C) : (A C) =>
HiddenHint (A : Prop) (B : Prop) : A B =>
"`left` oder `right`?"
Tactics left right assumption constructor rcases rfl contradiction trivial
NewTactics left right assumption constructor rcases rfl contradiction trivial

@ -21,4 +21,4 @@ Statement
: True := by
trivial
Tactics rw
NewTactics rw

@ -39,4 +39,4 @@ Statement mem_univ
trivial
-- tauto
Tactics tauto trivial
NewTactics tauto trivial

@ -39,7 +39,7 @@ Statement subset_empty_iff
intro h hA
apply mem_univ -- or `trivial`.
Tactics intro trivial apply
NewTactics intro trivial apply
-- blocked: tauto simp
end MySet

@ -54,8 +54,8 @@ Statement subset_empty_iff
rcases a with ⟨h₁, h₂⟩
assumption
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas 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 :)
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset
end MySet

@ -30,6 +30,6 @@ Statement nonempty_iff_ne_empty
push_neg
rfl
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -26,6 +26,6 @@ Statement
"" (A B : Set ) : (A ∅) ∩ B = A ∩ (univ ∩ B) := by
simp
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -30,6 +30,6 @@ Statement
rw [←union_diff_distrib]
rw [univ_union]
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -30,6 +30,6 @@ Statement
rw [←not_mem_compl_iff]
exact h4
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas 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
Lemmas in `import Mathlib.Data.Set`.
NewLemmas 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]
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics 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
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -32,6 +32,6 @@ Statement
({4, 9} : Set ) = Set.insert 4 {9} := by
rfl
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -35,5 +35,5 @@ Statement
simp_rw [mem_insert_iff, mem_singleton_iff] at *
tauto
Tactics simp_rw intro tauto rw
NewTactics simp_rw intro tauto rw
--Lemmas Subset.antisymm_iff empty_subset

@ -32,6 +32,6 @@ Statement
use 1
ring
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -37,6 +37,6 @@ Statement
assumption
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -36,6 +36,6 @@ Statement
ring
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -34,6 +34,6 @@ Statement
ring
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -28,6 +28,6 @@ Statement
{ x ∈ (S : Set ) | 0 ≤ x} ⊆ S := by
library_search
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -23,6 +23,6 @@ Statement
use 1
ring
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -22,6 +22,6 @@ open Set
Statement
"" : True := sorry
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -23,6 +23,6 @@ Statement
use 1
ring
Tactics constructor intro rw assumption rcases simp tauto trivial
NewTactics constructor intro rw assumption rcases simp tauto trivial
Lemmas Subset.antisymm_iff empty_subset
NewLemmas Subset.antisymm_iff empty_subset

@ -54,8 +54,7 @@ Statement
rw [←Set.union_diff_distrib]
rw [Set.univ_union]
Tactics rw
NewTactics rw
example : 4 ∈ (univ : Set ) := by
trivial

@ -35,4 +35,4 @@ lemma asdf (a b c d : ) (h₁ : c = d) (h₂ : a = b) (h₃ : a = d) : b = c
Conclusion ""
Tactics assumption
NewTactics assumption

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