reserve a,b,c,d,e for Real;
reserve X,Y for set,
          Z for non empty set,
          r for Real,
          s for ExtReal,
          A for Subset of REAL,
          f for real-valued Function;
reserve I for non empty closed_interval Subset of REAL,
       TD for tagged_division of I,
        D for Division of I,
        T for Element of set_of_tagged_Division(D),
        f for PartFunc of I,REAL;

theorem Th20:
  TD = [D,T] implies T = tagged_of TD &
  D = division_of TD
  proof
    assume
A1: TD = [D,T];
    ex D1 be Division of I, T1 be Element of set_of_tagged_Division(D1) st
      tagged_of(TD) = T1 & TD = [D1,T1] by Def2;
    hence thesis by A1,XTUPLE_0:1,COUSIN:def 6;
  end;
