 reserve R for finite Approximation_Space;
 reserve X,Y,Z for Subset of R;
 reserve kap for RIF of R;

theorem :: (19)
  (delta_2 R).(X,Y) = card (X \+\ Y) / card [#]R
  proof
A1: (CMap kappa_2 R).(X,Y) = card (X \ Y) / card [#]R by PropEx31;
A2: (CMap kappa_2 R).(Y,X) = card (Y \ X) / card [#]R by PropEx31;
    (delta_2 R).(X,Y) = (CMap kappa_2 R).(X,Y) + (CMap kappa_2 R).(Y,X)
      by Delta2
      .= (card (X \ Y) + card (Y \ X)) / card [#]R by XCMPLX_1:62,A1,A2
      .= card (X \+\ Y) / card [#]R by XBOOLE_1:82,CARD_2:40;
     hence thesis;
  end;
