theorem
  for x being set st x in dom f & 0 < max-f.x holds max+f.x = 0
proof
  let x be set;
  assume that
A1: x in dom f and
A2: 0 < max-f.x;
  0. < (max-(R_EAL f)).x by A2,Th30;
  then max+(R_EAL f).x = 0. by A1,MESFUNC2:16;
  hence thesis by Th30;
end;
