42 lines
949 B
Lean4
42 lines
949 B
Lean4
import Game.Levels.Power.Level_6
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World "Power"
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Level 7
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Title "pow_pow"
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open MyNat
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Introduction
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"
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Boss level! What will the collectible be?
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"
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/-- For all naturals $a$, $m$, $n$, we have $(a ^ m) ^ n = a ^ {mn}$. -/
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Statement MyNat.pow_pow
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(a m n : ℕ) : (a ^ m) ^ n = a ^ (m * n) := by
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induction n with t Ht
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· rw [mul_zero, pow_zero, pow_zero]
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rfl
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· rw [pow_succ, Ht, mul_succ, pow_add]
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rfl
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LemmaTab "Pow"
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attribute [simp] MyNat.pow_zero
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attribute [simp] MyNat.pow_succ
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attribute [simp] MyNat.pow_one
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attribute [simp] MyNat.one_pow
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attribute [simp] MyNat.pow_pow -- yes or no?
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Conclusion
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"
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Apparently Lean can't find a collectible, even though you feel like you
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just finished power world so you must have proved *something*. What should the
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collectible for this level be called?
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But what is this? It's one of those twists where there's another
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boss after the boss you thought was the final boss! Go to the next
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level!
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"
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