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import TestGame.Metadata
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import Std.Tactic.RCases
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import Mathlib.Tactic.LeftRight
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Game "TestGame"
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World "Contradiction"
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Level 2
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Title "Widerspruch"
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Introduction
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"
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Ähnlich siehts aus, wenn man Annahmen hat, die direkte Negierung voneinander sind,
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also `(h : A)` und `(g : ¬ A)`. (`\\not`)
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"
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Statement
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"Ein Widerspruch impliziert alles."
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(A : Prop) (n : ℕ) (h : ∃ x, 2 * x = n) (g : ¬ (∃ x, 2 * x = n)) : A := by
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contradiction
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Conclusion
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"
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Detail: `¬ A` ist übrigens als `A → false` implementiert, was aussagt, dass
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\"falls `A` wahr ist, impliziert das `false` und damit einen Widerspruch\".
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"
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-- TODO: Oder doch ganz entfernen?
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Tactics contradiction
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