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

theorem :: Proposition 5
  X <> {} implies
    kappa (X,Y) = ((CMap kappa_1 R).(X,Y`)) / (kappa_1 (Y`,X))
                = ((CMap kappa_2 R).(X,Y`)) / (kappa_2 ([#]R,X))
  proof
    assume
A0: X <> {}; then
    kappa (X,Y) = ((CMap kappa_1 R).(X,Y`)) / (kappa_1 (Y`,X)) by Lemma1;
    hence thesis by A0,Lemma2;
  end;
