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import Adam.Metadata
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import Std.Tactic.RCases
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import Mathlib.Tactic.Cases
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import Mathlib
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Game "Adam"
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World "Implication"
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Level 11
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Title "by_cases"
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Introduction
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"
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**Du**: Sagt mal, hätte ich da nicht auch einfach zwei Fälle anschauen können:
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Wenn `A` wahr ist, beweis ich die rechte Seite, sonst die Linke.
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**Robo**: Tatsächlich, `by_cases h : A` würde genau das machen!
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"
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Statement (A : Prop) : ¬A ∨ A := by
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Hint (hidden := true) "**Du**: Wie?
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**Robo**: Also `by_cases h : A` erstellt zwei Goals. Im ersten hast Du `(h : A)` zur
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Verfügung, im zweiten `(h : ¬ A)`."
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by_cases h : A
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Hint "**Du**: "
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right
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assumption
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left
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assumption
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Conclusion
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"
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**Du**: Das kann noch ganz nützlich sein.
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"
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NewTactic by_cases
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DisabledTactic tauto
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