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

theorem Th5:
  A, A` constitute_a_decomposition
proof
  A misses A` & A \/ A` = [#]X by PRE_TOPC:2,XBOOLE_1:79;
  hence A, A` constitute_a_decomposition;
end;
