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 upper UniformSpaceStr, R being Relation of the carrier of US
  st the entourages of US = rho(R) &
  meet the entourages of US in the entourages of US holds
  the entourages of US = rho(meet the entourages of US) by Th31;
