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import TestGame.Metadata
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Game "TestGame"
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World "Old"
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Level 2
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Title "The rewriting spell"
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Introduction
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"
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The rewrite spell is the way to \"substitute in\" the value
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of an expression. In general, if you have a hypothesis of the form `A = B`, and your
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goal mentions the left hand side `A` somewhere, then
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the `rewrite` tactic will replace the `A` in your goal with a `B`.
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The documentation for `rewrite` just appeared in your spell book.
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Play around with the menus and see what is there currently.
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More information will appear as you progress.
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Take a look in the top right box at what we have.
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The variables $x$ and $y$ are natural numbers, and we have
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an assumption `h` that $y = x + 7$. Our goal
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is to prove that $2y=2(x+7)$. This goal is obvious -- we just
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substitute in $y = x+7$ and we're done. In Lean, we do
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this substitution using the `rewrite` spell. This spell takes a list of equalities
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or equivalences so you can cast `rewrite [h]`.
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"
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Statement (x y : ℕ) (h : y = x + 7) : 2 * y = 2 * (x + 7) := by
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rewrite [h]
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rfl
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Message (x : ℕ) (y : ℕ) (h : y = x + 7) : 2*(x + 7) = 2*(x + 7) =>
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"Great! Now the goal should be easy to reach using the `rfl` spell."
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Conclusion "Congratulations for completing your second level!"
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Tactics rfl rewrite
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