theorem Th60:
  (Infty_dist n).(x,y) = (Infty_dist n).(y,x)
  proof
    (Infty_dist n).(x,y) = sup rng abs(x-y) &
    (Infty_dist n).(y,x) = sup rng abs(y-x) by Def7;
    hence (Infty_dist n).(x,y) = (Infty_dist n).(y,x) by Th1;
  end;
