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;
reserve f for Function of I,REAL;

theorem Th25:
  I is non empty trivial implies vol I = 0
  proof
    assume I is non empty trivial;
    then consider x be object such that
A1: I = {x} by ZFMISC_1:131;
    x in I by A1,TARSKI:def 1;
    then reconsider x as Real;
    vol {x} = 0 by COUSIN:41;
    hence thesis by A1;
  end;
