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

theorem Th8:
  for A being Subset of T holds Int(A /\ Cl A`) = {} T
proof
  let A be Subset of T;
A1: Int A misses (Int A)` by XBOOLE_1:79;
  thus Int(A /\ Cl A`) = Int(A /\ ((Cl A`)`)`)
    .= Int(A /\ (Int A)`) by TOPS_1:def 1
    .= Int Int A /\ Int((Int A)`) by TOPS_1:17
    .= Int(Int A /\ (Int A)`) by TOPS_1:17
    .= Int({} T) by A1
    .= {} T;
end;
