
theorem
for X be non empty set, S be SigmaField of X, M be sigma_Measure of S,
 f be nonnegative PartFunc of X, ExtREAL
 holds integral'(M,max-(-f)) = integral'(M,f)
proof
   let X be non empty set, S be SigmaField of X, M be sigma_Measure of S,
   f be nonnegative PartFunc of X, ExtREAL;
   -f = -(max-(-f)) by Th32; then
   f = -(-max-(-f)) by Th36; then
   f = (-1)(#)(-max-(-f)) by MESFUNC2:9; then
   f = (-1)(#)((-1)(#)(max-(-f))) by MESFUNC2:9; then
   f = ((-1)*(-1))(#)(max-(-f)) by Th35;
   hence integral'(M,max-(-f)) = integral'(M,f) by MESFUNC2:1;
end;
