average33 : [32] -> [32] -> [32]
average33 x y = drop`{1}(z'/2)
    where
          z' : [33]
          z' = (0b0 # x) + (0b0 # y)

average1 : [32] -> [32] -> [32]
average1 x y = (x + y)/2

average2 : [32] -> [32] -> [32]
average2 x y = x/2 + y/2 + (x%2 && y%2)

average3 : [32] -> [32] -> [32]
average3 x y = (x + y) >> 1

average4 : [32] -> [32] -> [32]
average4 x y =    (x >> 1) + (y >> 1) + (x && y && 1)

average5 : [32] -> [32] -> [32]
average5 x y = lo + ((hi - lo)>>1) where
    lo = min x y
    hi = max x y

property av1 x y = average33 x y == average1 x y
property av2 x y = average33 x y == average2 x y
property av3 x y = average33 x y == average3 x y
property av4 x y = average33 x y == average4 x y
property av5 x y = average33 x y == average5 x y

property applesOranges x y = average4 x y == average5 x y