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22 lines
396 B
Plaintext
22 lines
396 B
Plaintext
import NNG.MyNat.Definition
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namespace MyNat
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open MyNat
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def pow : MyNat → MyNat → MyNat
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| _, zero => one
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| m, (succ n) => pow m n * m
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instance : Pow MyNat MyNat where
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pow := pow
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-- notation a ^ b := pow a b
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example : (1 : MyNat) ^ (1 : MyNat) = 1 := rfl
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lemma pow_zero (m : MyNat) : m ^ (0 : MyNat) = 1 := rfl
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lemma pow_succ (m n : MyNat) : m ^ (succ n) = m ^ n * m := rfl
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end MyNat
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