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

theorem Th4:
  A1 = A2` or A2 = A1` implies A1,A2 constitute_a_decomposition
proof
  assume A1 = A2` or A2 = A1`;
  then A1 misses A2 & A1 \/ A2 = [#]X by SUBSET_1:23,TDLAT_1:1;
  hence thesis;
end;
