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

data List : Type -> Type where
     Nil : List $a
     Cons : $a -> List $a -> List $a

data Pair : Type -> Type -> Type where
     MkPair : $a -> $b -> Pair $a $b

data Elem : $a -> List (Pair $a $b) -> Type where
     Here : Elem $x (Cons (MkPair $x $y) $xs)
     There : Elem $x $xs -> Elem $x (Cons $y $xs)

fst : {0 a, b : _} -> Pair a b -> a
fst (MkPair $x _) = x

snd : {0 a, b : _} -> Pair a b -> b
snd (MkPair _ $y) = y

%pair Pair fst snd

getNth : (x : $a) -> (xs : List (Pair $a $b)) -> Elem x xs -> $b
getNth $x (Cons (MkPair $x $y) $xs) Here = y
getNth $x (Cons _ $xs) (There $p) = getNth x xs p

getNth' : (x : $a) -> (xs : List (Pair $a $b)) -> 
          {auto prf : Elem x xs} -> $b
getNth' $x $xs {prf = $prf} = getNth x xs prf