 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 Kappa1RIF4:
  kappa_1 (X,Y) = 0 implies X misses Y
  proof
    assume
A1: kappa_1 (X,Y) = 0;
    per cases;
    suppose X <> {}; then
      Y = {} by A1,Prop4a;
      hence thesis;
    end;
    suppose X = {};
      hence thesis;
    end;
  end;
