[copascetic]

When you specify the types of the numbers used, so that you are testing the transitivity of a single instance of Eq, you will find that transitivity does hold in this case.

  a :: Double
  a = 2^53

  b :: Double
  b = 2.0^53

  c :: Double
  c = 2^53 + 1

  main :: IO ()
  main = do
    print $ a == b -- True
    print $ b == c -- True
    print $ a == c -- True