theorem Th62:
  Infty_dist n is_metric_of REAL n
  proof
    for x,y,z be Element of REAL n holds
       ((Infty_dist n).(x,y) = 0 iff x = y) &
       ((Infty_dist n).(x,y) = (Infty_dist n).(y,x)) &
       ((Infty_dist n).(x,z) <= (Infty_dist n).(x,y) + (Infty_dist n).(y,z))
      by Th59,Th60,Th61;
    hence thesis by PCOMPS_1:def 6;
  end;
