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import TestGame.Metadata
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import Mathlib
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Game "TestGame"
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World "Predicate"
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Level 4
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Title "Rewrite"
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Introduction
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"
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Mit `rw` kann man nicht nur das Goal sondern auch andere Annahmen umschreiben:
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Wenn `(h : X = Y)` ist, dann ersetzt `rw [h] at g` in der Annahme
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`g` das `X` durch `Y`.
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"
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Statement umschreiben
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"Angenommen man hat die Gleichheiten
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$$
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\\begin{aligned} a &= b \\\\ a + a ^ 2 &= b + 1 \\end{aligned}
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$$
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Zeige dass $b + b ^ 2 = b + 1$."
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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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rw [h] at g
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assumption
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Message (a : ℕ) (b : ℕ) (h : a = b) (g : a + a ^ 2 = b + 1) : b + b ^ 2 = b + 1 =>
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"`rw [ ... ] at g` schreibt die Annahme `g` um."
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Message (a : ℕ) (b : ℕ) (h : a = b) (g : a + a ^ 2 = b + 1) : a + a ^ 2 = a + 1 =>
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"Sackgasse. probiers doch mit `rw [h] at g` stattdessen."
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Conclusion "Übrigens, mit `rw [h] at *` kann man im weiteren `h` in **allen** Annahmen und
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dem Goal umschreiben."
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Tactics assumption rw
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