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import Adam.Metadata
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import Mathlib
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Game "Adam"
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World "Predicate"
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Level 3
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Title "Rewrite"
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Introduction
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"
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**Evenine**: Mit diesem neuen Wissen, könnt ihr mir bei folgendem helfen:
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"
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Statement
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"
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$$
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\\begin{aligned}
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a &= b \\\\
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a + a ^ 2 &= b + 1 \\\\
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\\vdash b + b ^ 2 = b + 1
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\\end{aligned}
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$$
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"
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(a b : ℕ) (h : a = b) (g : a + a ^ 2 = b + 1) : b + b ^ 2 = b + 1 := by
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Hint "**Du**: Ah da ersetzt man ja einfach `{a}` durch `{b}` in der anderen Annahme!
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**Robo**: Genau! Das machst du mit `rw [{h}] at {g}`."
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rw [h] at g
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Hint (hidden := true) "**Robo**: Schau mal durch die Annahmen."
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assumption
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Conclusion "
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**Robo**: Noch ein Trick: Mit `rw [h] at *` kann man im weiteren `h` in **allen** Annahmen und
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dem Goal umschreiben.
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"
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