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

theorem Th31:
  for T being TopSpace holds Closed_Domains_of T c= Domains_of T
  proof
    let T be TopSpace;
    let x be object;
    assume x in Closed_Domains_of T; then
    x in { A where A is Subset of T : A is closed_condensed }; then
    consider A1 being Subset of T such that
A1: x = A1 & A1 is closed_condensed;
    A1 is condensed by A1,TOPS_1:66; then
    x in { A where A is Subset of T : A is condensed } by A1;
    hence thesis;
  end;
