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import TestGame.Metadata
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import Mathlib.Tactic.Ring
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Game "TestGame"
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World "Predicate"
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Level 5
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Title "Natürliche Zahlen"
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Introduction
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"
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Ring setzt aber nicht selbständig Annahmen ein, diese muss man zuerst manuell mit `rw` verwenden.
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"
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Statement
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"Angenommen, man hat die Gleichung $x = 2 * y + 1$, zeige
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$x ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y$. "
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(x y : ℕ) (h : x = 2 * y + 1) : x ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y := by
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rw [h]
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ring
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Message (x : ℕ) (y : ℕ) (h : x = 2 * y + 1) : x ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y =>
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"Die Annahme `h` kannst du mit `rw [h]` benützen."
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Message (y : ℕ) : (2 * y + 1) ^ 2 = 4 * y ^ 2 + 3 * y + 1 + y =>
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"Jetzt kann `ring` übernehmen."
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Conclusion ""
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Tactics ring rw
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