  We show a surprising connexion between a property of the inf convolution of a
family of convex lower semicontinuous functions and the fact that the
intersection of maximal cyclically monotone graphs is the critical set of a
bipotential.
  We then extend the results from arXiv:math/0608424v4 to bipotentials convex
covers, generalizing the notion of a bi-implicitly convex lagrangian cover.
  As an application we prove that the bipotential related to Coulomb's friction
law is related to a specific bipotential convex cover with the property that
any graph of the cover is non maximal cyclically monotone.
