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

theorem
  X <> {} implies (CMap kappa R).(X,Y) = kappa (X, Y`)
  proof
    assume
A0: X <> {};
    (CMap kappa R).(X,Y) = 1 - (kappa R).(X,Y) by CDef
       .= 1 - kappa (X,Y) by ROUGHIF1:def 2;
    hence thesis by A0,ROUGHIF1:35;
  end;
