reserve r,p,x for Real;
reserve n for Element of NAT;
reserve A for non empty closed_interval Subset of REAL;
reserve Z for open Subset of REAL;

theorem
  for f being PartFunc of REAL,REAL,
  A being non empty closed_interval Subset of
  REAL st (f(#)f)||A is total & (f(#)f)||A|A is bounded & (f(#)f)||A is
integrable & (for x st x in A holds (f(#)f)||A.x >= 0) holds |||(f,f,A)||| >= 0
  by INTEGRA2:32;
