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