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44 lines
1.3 KiB
Plaintext
44 lines
1.3 KiB
Plaintext
import NNG.Metadata
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Game "NNG"
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World "Function"
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Level 9
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Title ""
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open MyNat
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Introduction
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"
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I asked around on Zulip and apparently there is not a tactic for this, perhaps because
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this level is rather artificial. In world 6 we will see a variant of this example
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which can be solved by a tactic. It would be an interesting project to make a tactic
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which could solve this sort of level in Lean.
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You can of course work both forwards and backwards, or you could crack and draw a picture.
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"
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Statement
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"Given a bunch of functions, we can define another one."
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(A B C D E F G H I J K L : Type)
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(f1 : A → B) (f2 : B → E) (f3 : E → D) (f4 : D → A) (f5 : E → F)
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(f6 : F → C) (f7 : B → C) (f8 : F → G) (f9 : G → J) (f10 : I → J)
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(f11 : J → I) (f12 : I → H) (f13 : E → H) (f14 : H → K) (f15 : I → L) : A → L := by
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Hint "In any case, start with `intro a`!"
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intro a
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Hint "Now use a combination of `have` and `apply`."
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apply f15
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apply f11
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apply f9
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apply f8
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apply f5
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apply f2
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apply f1
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exact a
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Conclusion
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"
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That's the end of Function World! Next it's Proposition world, and the tactics you've learnt in Function World are enough
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to solve all nine levels! In fact, the levels in Proposition world might look strangely familiar$\\ldots$.
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"
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