
theorem
for X be non empty set, f be nonnegative PartFunc of X,ExtREAL holds f = max+f
proof
   let X be non empty set, f be nonnegative PartFunc of X,ExtREAL;
b3:dom f = dom(max+f) by MESFUNC2:def 2;
   for x be Element of X st x in dom f holds f.x = (max+f).x
   proof
    let x be Element of X;
    assume b2: x in dom f;
    max(f.x,0) = f.x by SUPINF_2:51,XXREAL_0:def 10;
    hence f.x = (max+f).x by b2,b3,MESFUNC2:def 2;
   end;
   hence f = max+f by b3,PARTFUN1:5;
end;
