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,MESFUNC2:15;
  hence thesis by Th30;
end;
