
theorem Th34: :: theorem 5.2, p. 189
  for n being Element of NAT, N being Subset of RelStr(#Bags n,
    DivOrder n#) ex B being finite Subset of Bags n st B is_Dickson-basis_of N,
  RelStr(#Bags n, DivOrder n#)
proof
  let n be Element of NAT, N be Subset of RelStr(#Bags n, DivOrder n#);
  consider B being set such that
A1: B is_Dickson-basis_of N,RelStr(#Bags n, DivOrder n#) and
A2: B is finite by DICKSON:def 10;
  now
    let u be object;
    assume
A3: u in B;
    B c= N by A1,DICKSON:def 9;
    hence u in N by A3;
  end;
  then reconsider B as finite Subset of N by A2,TARSKI:def 3;
  reconsider B as finite Subset of Bags n by XBOOLE_1:1;
  take B;
  thus thesis by A1;
end;
