 reserve R for 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite 1-sorted;
 reserve X,Y for Subset of R;
 reserve R for finite Approximation_Space;
 reserve X,Y,Z,W for Subset of R;

theorem :: Proposition 4 h)
  X \/ Y = [#]R implies kappa_1(X,Y) = kappa_2(X,Y)
  proof
    assume
AB: X \/ Y = [#]R;
    X`` \/ Y = [#]R by AB; then
F1: card Y = card (X` \/ Y) by XBOOLE_1:12,LemmaSet;
    per cases;
    suppose
      X \/ Y <> {};
      thus thesis by F1,AB,Kappa1;
    end;
    suppose X \/ Y = {};
      hence thesis by AB;
    end;
  end;
