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

theorem PropEx30:
  X \/ Y = {} implies (CMap kappa_1 R).(X,Y) = 0
  proof
    assume
AA: X \/ Y = {};
A1: (kappa_1 R).(X,Y) = kappa_1 (X,Y) by ROUGHIF1:def 5 .= 1
      by AA,ROUGHIF1:def 3;
    (CMap kappa_1 R).(X,Y) = 1 - (kappa_1 R).(X,Y) by CDef
        .= 0 by A1;
    hence thesis;
  end;
