theorem
  max+f is nonnegative & max-f is nonnegative
proof
  for x be object st x in dom max+f holds 0 <= max+f.x by RFUNCT_3:37;
  hence max+f is nonnegative by Th52;
  for x be object st x in dom max-f holds 0 <= max-f.x by RFUNCT_3:40;
  hence thesis by Th52;
end;
