36 lines
1 KiB
Text
36 lines
1 KiB
Text
abbrev ℕ := Nat
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def hyperoperation : ℕ → ℕ → ℕ → ℕ
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| 0, _, k => k + 1
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| 1, m, 0 => m
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| 2, _, 0 => 0
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| _ + 3, _, 0 => 1
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| n + 1, m, k + 1 => hyperoperation n m (hyperoperation (n + 1) m k)
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attribute [local grind] hyperoperation
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@[grind =]
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theorem hyperoperation_zero (m k : ℕ) : hyperoperation 0 m k = k + 1 := by
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grind
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@[grind =]
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theorem hyperoperation_recursion (n m k : ℕ) :
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hyperoperation (n + 1) m (k + 1) = hyperoperation n m (hyperoperation (n + 1) m k) := by
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grind
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@[grind =]
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theorem hyperoperation_one (m k : ℕ) : hyperoperation 1 m k = m + k := by
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induction k with grind
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@[grind =]
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theorem hyperoperation_two (m k : ℕ) : hyperoperation 2 m k = m * k := by
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induction k with grind
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@[grind =]
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theorem hyperoperation_three (m k : ℕ) : hyperoperation 3 m k = m ^ k := by
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induction k with grind
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@[grind =] theorem hyperoperation_ge_three_one (n k : ℕ) : hyperoperation (n + 3) 1 k = 1 := by
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induction n generalizing k with
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| zero => grind
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| succ n ih => cases k <;> grind
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