theorem
  Pitag_dist 1 = Infty_dist 1
  proof
    now
      let x,y being set;
      assume x in REAL 1 & y in REAL 1;
      then reconsider x1 = x, y1 = y as Element of REAL 1;
      thus (Pitag_dist 1).(x,y) = |.x1.1-y1.1.| by Th66
                               .= (Infty_dist 1).(x,y) by Th65;
    end;
    hence thesis by BINOP_1:def 21;
  end;
