JL writes,

   A formal treatment of parametricity in the presence of overloading
   has not been written up (Eric Meijer has talked of doing so). The
   problem with writing it up is that it's too simple: it reduces to a
   single observation, namely that the parametricity theorem coming
   from an overloaded type is the regular parametricity theorem that
   arises after performing the dictionary expansion.

You can find this observation in Section 3.4 of the original
`Theorems for Free'.  So it is written up!  -- P

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