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;
reserve SF for Subset-Family of X, A for Element of SF;

theorem Th34:
  A = {} implies block_Pervin_uniformity(A) = [:X,X:]
  proof
    assume A = {};
    then block_Pervin_uniformity(A) = [:X \ {},X \ {}:] \/ [:{},{}:];
    hence thesis;
  end;
