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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 7
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Title "Schnittmenge und Vereinigung"
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Introduction
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"
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Die klassischen Mengenoperationen sind
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Schnittmenge `∩` (`\\inter`), Vereinigung `∪` (`\\union`) und
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Differenz `\\` (`\\\\`).
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Die Taktik `simp` kann triviale Aussagen with Vereinigung mit der
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leeren Menge vereinfachen.
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"
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open Set
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Statement
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"" (A B : Set ℕ) : (A ∪ ∅) ∩ B = A ∩ (univ ∩ B) := by
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simp
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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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