theorem
  for x being set st x in dom f & max+f.x = f.x holds max-f.x = 0
proof
  let x be set;
  assume that
A1: x in dom f and
A2: max+f.x =f.x;
  f.x = max+(R_EAL f).x by A2,Th30;
  then max-(R_EAL f).x = 0. by A1,MESFUNC2:19;
  hence thesis by Th30;
end;
