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import Adam.Metadata
import Mathlib.Data.Set.Basic
set_option tactic.hygienic false
Game "Adam"
World "SetTheory"
Level 7
Title "Schnittmenge und Vereinigung"
Introduction
"
Die klassischen Mengenoperationen sind
Schnittmenge `∩` (`\\inter`), Vereinigung `∪` (`\\union`) und
Differenz `\\` (`\\\\`).
Die Taktik `simp` kann triviale Aussagen with Vereinigung mit der
leeren Menge vereinfachen.
"
open Set
Statement
"" (A B : Set ℕ) : (A ∪ ∅) ∩ B = A ∩ (univ ∩ B) := by