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

theorem
  A1,A2 constitute_a_decomposition & B1,B2 constitute_a_decomposition
  implies (A1 \/ B1),(A2 /\ B2) constitute_a_decomposition by Th13;
