reserve X for non empty 1-sorted;
reserve A, A1, A2, B1, B2 for Subset of X;
reserve X for non empty TopSpace;
reserve A, A1, A2, B1, B2 for Subset of X;

theorem
  for A1, A2 being Subset of X st A1,A2 constitute_a_decomposition holds
  (A1 is closed iff A2 is open) by Th11;
