reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;

theorem
  for A, B being Subset of T st A is open_condensed & B is
  open_condensed holds Cl A c= Cl B iff A c= B
proof
  let A, B be Subset of T;
  assume that
A1: A is open_condensed and
A2: B is open_condensed;
  thus Cl A c= Cl B implies A c= B
  proof
    assume Cl A c= Cl B;
    then
A3: Int Cl A c= Int Cl B by TOPS_1:19;
    Int Cl A = A by A1,TOPS_1:def 8;
    hence thesis by A2,A3,TOPS_1:def 8;
  end;
  thus thesis by PRE_TOPC:19;
end;
