reserve T for 1-sorted;
reserve T for TopSpace;

theorem Th16:
  for A being Subset of T st A is condensed holds A` is condensed
proof
  let X be Subset of T;
  assume
A1: X is condensed;
  then X c= Cl Int X by TOPS_1:def 6;
  then (Cl(Int X)``)` c= X` by SUBSET_1:12;
  then Int(Int X)` c= X` by TOPS_1:def 1;
  then
A2: Int(Cl X`)`` c= X` by TOPS_1:def 1;
  Int Cl X c= X by A1,TOPS_1:def 6;
  then (Cl((Cl X)`))` c= X by TOPS_1:def 1;
  then X` c= Cl(Cl(X``))` by SUBSET_1:12;
  then X` c= Cl(Int X`) by TOPS_1:def 1;
  hence thesis by A2,TOPS_1:def 6;
end;
