reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;

theorem Th6:
  for A being Subset of X st A is closed holds Int(A \/ B) = Int(A \/ Int B)
proof
  let A be Subset of X;
  A \/ Int B c= A \/ B by TOPS_1:16,XBOOLE_1:9;
  then
A1: Int(A \/ Int B) c= Int(A \/ B) by TOPS_1:19;
  assume A is closed;
  then Int Int(A \/ B) c= Int(A \/ Int B) by Th5,TOPS_1:19;
  hence thesis by A1;
end;
