Let . The equations derived in part (e) become and , where . Replacing zero and successor by that seed and step is exactly a natural-number fold:
twoFibsNat :: Natural -> (Integer, Integer)
twoFibsNat = foldNat step (0, 1)
  where
    step :: (Integer, Integer) -> (Integer, Integer)
    step (a, b) = (b, a + b)

fibNat :: Natural -> Integer
fibNat = fst . twoFibsNat
Consequently
(1)
Structural induction follows the constructors of Natural: the seed gives the first two Fibonacci numbers, and the successor step uses the Fibonacci recurrence. The extra component carries exactly the information needed for the next update.

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