data Nat : Type where
     Z : Nat
     S : Nat -> Nat

simpleAs : Nat -> Nat
simpleAs z@(_) = z

as : Nat -> Nat
as Z = Z
as p@(S $k) = p

plus : Nat -> Nat -> Nat
plus Z $y = y
plus (S $k) $y = S (plus k y)

data PairNat : Type where
     MkPair : Nat -> Nat -> PairNat

pairPred : Nat -> PairNat
pairPred Z = MkPair Z Z
pairPred (S Z) = MkPair Z Z
pairPred (S p@(S $k)) = MkPair p k