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;

theorem
  UniCl D is Ring_of_sets
  proof
    set DU = the set of all union P where P is Subset of D;
    UniCl D is cap-closed cup-closed;
    then DU is cap-closed cup-closed by Th14;
    then for x,y be set st x in DU & y in DU holds x/\y in DU & x\/y in DU;
    then DU is Ring_of_sets by COHSP_1:def 7,LATTICE7:def 8;
    hence thesis by Th14;
  end;
