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import NNG.MyNat.Multiplication
namespace MyNat
open MyNat
def pow : ℕ → ℕ → ℕ
| _, zero => one
| m, (succ n) => pow m n * m
instance : Pow ℕℕ where
pow := pow
-- notation a ^ b := pow a b
example : (1 : ℕ) ^ (1 : ℕ) = 1 := rfl
lemma pow_zero (m : ℕ) : m ^ (0 : ℕ) = 1 := rfl
lemma pow_succ (m n : ℕ) : m ^ (succ n) = m ^ n * m := rfl