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

theorem Th9:
  for A being Subset of T holds Cl(A \/ Int A`) = [#] T
proof
  let A be Subset of T;
  thus Cl(A \/ Int A`) = Cl(A \/ (Cl(A``))`) by TOPS_1:def 1
    .= Cl Cl A \/ Cl (Cl A)` by PRE_TOPC:20
    .= Cl(Cl A \/ (Cl A)`) by PRE_TOPC:20
    .= Cl([#] T) by PRE_TOPC:2
    .= [#] T by TOPS_1:2;
end;
