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

theorem PropEx3k0:
  X = {} implies (CMap kappa R).(X,Y) = 0
  proof
    assume
A1: X = {};
G1: kappa (X,Y) = 1 by ROUGHIF1:6,A1,XBOOLE_1:2;
    (CMap kappa R).(X,Y) = 1 - (kappa R).(X,Y) by CDef
      .= 1 - kappa (X,Y) by ROUGHIF1:def 2
      .= 0 by G1;
    hence thesis;
  end;
