30 lines
1.1 KiB
Lean4
30 lines
1.1 KiB
Lean4
import Game.Levels.Power.Level_8
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World "Power"
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Title "Power World"
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Introduction
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"
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A new world with seven levels. And a new import!
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This import gives you the power to make powers of your
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natural numbers. It is defined by recursion, just like addition and multiplication.
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Here are the two new axioms:
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* `pow_zero (a : ℕ) : a ^ 0 = 1`
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* `pow_succ (a b : ℕ) : a ^ succ b = a ^ b * a`
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The power function has various relations to addition and multiplication.
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If you have gone through levels 1--6 of addition world and levels 1--9 of
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multiplication world, you should have no trouble with this world:
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The usual tactics `induction`, `rw` and `rfl` should see you through.
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You should probably look at your inverntory again: addition and multiplication
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have a solid API by now, i.e. if you need something about addition
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or multiplication, it's probably already in the library we have built.
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Collectibles are indication that we are proving the right things.
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The levels in this world were designed by Sian Carey, a UROP student
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at Imperial College London, funded by a Mary Lister McCammon Fellowship,
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in the summer of 2019. Thanks Sian!
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"
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