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;
reserve f,g for HK-integrable Function of I,REAL,
          r for Real;

theorem Th36:
  for f being Function of I,REAL st f is constant holds
  (f is HK-integrable & ex r being Real st
  f = r (#) chi(I,I) & HK-integral f = r * vol(I))
  proof
    let f be Function of I,REAL;
    assume f is constant;
    then consider r be Real such that
A1: f = r (#) chi(I,I) by Th16;
    reconsider g = chi(I,I) as Function of I,REAL by Th11;
A2: g is HK-integrable & HK-integral(g) = vol(I) by Th30;
    hence f is HK-integrable by A1,Th35;
    take r;
    thus thesis by A1,A2,Th35;
  end;
