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 Th37:
  basis_Pervin_uniformity(SF) is quasi_basis
  proof
    basis_Pervin_uniformity(SF) is cap-closed by Th36;
    hence thesis;
  end;
