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

theorem Prop6e2: :: Proposition 6 e2)
  0 <= (CMap kappa_2 R).(X,Y) + (CMap kappa_2 R).(Y,X) <= 1
  proof
    (CMap kappa_2 R).(X,Y) + (CMap kappa_2 R).(Y,X) =
      card (X \ Y) / card [#]R + (CMap kappa_2 R).(Y,X) by PropEx31
      .= card (X \ Y) / card [#]R + card (Y \ X) / card [#]R by PropEx31
      .= (card (X \ Y) + card (Y \ X)) / card [#]R by XCMPLX_1:62
      .= card (X \+\ Y) / card [#]R by CARD_2:40,XBOOLE_1:82;
    hence thesis by NAT_1:43,XREAL_1:183;
  end;
