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lean4game/server/testgame/TestGame/Levels/SetTheory/L08_UnionInter.lean

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import TestGame.Metadata
import Mathlib.Data.Set.Basic
set_option tactic.hygienic false
Game "TestGame"
World "SetTheory"
Level 8
Title "Schnittmenge und Vereinigung"
Introduction
"
Ansonsten gibt es jegliche Lemmas in
`import Mathlib.Data.Set.Basic`
die beim Umgang mit diesen Operationen weiterhelfen. Schaue in der Bibliothek auf
der Seite nach Lemmas, die dir hier weiterhelfen!
"
open Set
Statement
""
(A B : Set ) : univ \ (A ∩ B) = (univ \ A) (univ \ B) (A \ B) := by
rw [diff_inter]
rw [union_assoc]
rw [←union_diff_distrib]
rw [univ_union]
NewTactics constructor intro rw assumption rcases simp tauto trivial
NewLemmas Subset.antisymm_iff empty_subset