theorem
  for x being set st x in dom f & max-f.x = 0 holds max+f.x = f.x
proof
  let x be set;
  assume that
A1: x in dom f and
A2: max-f.x =0;
  0 = max-(R_EAL f).x by A2,Th30;
  then max+(R_EAL f).x = (R_EAL f).x by A1,MESFUNC2:22;
  hence thesis by Th30;
end;
