theorem
  f is_integrable_on M implies |. Integral(M,f).| <= Integral(M,abs f)
proof
  assume f is_integrable_on M;
  then R_EAL f is_integrable_on M;
  then |. Integral(M,f) .| <= Integral(M,|. R_EAL f .|) by MESFUNC5:101;
  hence thesis by Th1;
end;
