theorem
  for f, g being Element of NAT st f + (z,T) = g + (z,T)
   holds f = g
proof
  let f, g be Element of NAT;
  assume f + (z,T) = g + (z,T);
  then locnum(f,T) + z = locnum(g,T) + z by Th5;
  hence thesis by Th7;
end;
