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import prelude
data Nat : Type where
Zero : Nat
Succ : (n:Nat) -> Nat
add_Nat : Add Nat
add_Nat = rec zero = Zero
plus = natPlus
natPlus : Nat -> Nat -> Nat
natPlus Zero y = y
natPlus (Succ x) y = Succ (natPlus x y)
pred : Nat -> Nat
pred Zero = Zero
pred (Succ n) = n
natToInt : Nat -> Integer
natToInt Zero = 0
natToInt (Succ n) = 1 + natToInt n
intToNat : Integer -> Nat
intToNat n = if n == 0 then Zero else Succ (intToNat (n-1))
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