  Recently, we have derived the changes in the absorption spectrum of an
exciton when this exciton is photocreated close to a metal. The resolution of
this problem -- which has similarities with Fermi edge singularities -- has
been made possible by the introduction of ``exciton diagrams''. The validity of
this procedure relied on a dreadful calculation based on standard free electron
and free hole diagrams, with the semiconductor-metal interaction included at
second order only, and its intuitive extention to higher orders. Using the
commutation technique we recently introduced to deal with interacting excitons,
we are now able to \emph{prove} that this exciton diagram procedure is indeed
valid at any order in the interaction.
  =
