theorem
  for f, g being Element of NAT st NextLoc(f,T) = NextLoc(g,T)
  holds f = g
proof
  let f, g be Element of NAT such that
A1: NextLoc(f,T) = NextLoc(g,T);
  set m = locnum(g,T);
  set k = locnum(f,T);
  k+0 = k+1-1
    .= m+1-1 by A1,Th5
    .= m+0;
  hence thesis by Th7;
end;
