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import TestGame.Metadata
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import Mathlib
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import Mathlib.Algebra.Parity
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import Mathlib.Tactic.Ring
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Game "TestGame"
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World "SetTheory2"
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Level 3
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Title ""
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Introduction
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"
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Um anzunehmen, dass zwei Mengen disjunkt sind schreibt man
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`Disjoint S T`, welches dadurch definiert ist das die
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einzige gemeinsame Teilmenge die leere Menge ist,
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also etwa `A ⊆ S → A ⊆ T → A ⊆ ∅`.
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Beachte, dass `Disjoint` in Lean genereller definiert ist als
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für Mengen, deshalb siehst du die Symbole
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`≤` anstatt `⊆` und `⊥` anstatt `∅`, aber diese bedeuten genau
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das gleiche.
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"
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open Set
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Statement
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"" :
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¬Disjoint ({n : ℤ | ∃ k, n = 2 * k} : Set ℤ) ({3, 5, 6, 9, 11} : Set ℤ) := by
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unfold Disjoint
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rw [not_forall] -- why not `push_neg`?
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use {6}
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simp
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use 3
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ring
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Tactics constructor intro rw assumption rcases simp tauto trivial
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Lemmas Subset.antisymm_iff empty_subset
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