reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;
reserve US for UniformSpace;
reserve R for Relation of X;

theorem
  for US being UniformSpaceStr holds
  the carrier of RelStr2UniformSpaceStr(UniformSpaceStr2RelStr(US)) =
    the carrier of US &
  the entourages of RelStr2UniformSpaceStr(UniformSpaceStr2RelStr(US)) =
    rho(meet the entourages of US);
