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 R being Tolerance of X holds
  uniformity_induced_by(R) is Semi-UniformSpace &
  the entourages of uniformity_induced_by(R) = rho(R) &
  meet the entourages of uniformity_induced_by(R) = R by Th28;
