theorem
  Pitag_dist 2 <> Infty_dist 2
  proof
    set x = |[0,0]|, y = |[1,1]|;
    now
      take x,y;
      x is Element of REAL 2 & y is Element of REAL 2 by  EUCLID:22;
      hence x in REAL 2 & y in REAL 2;
      thus (Pitag_dist 2).(x,y) <> (Infty_dist 2).(x,y)
        by Th63,Th64,SQUARE_1:19;
    end;
    hence thesis;
  end;
