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

theorem Th8:
  A1,A constitute_a_decomposition & A,A2 constitute_a_decomposition
  implies A1 = A2
proof
  assume A1,A constitute_a_decomposition;
  then
A1: A1 = A` by Th3;
  assume A,A2 constitute_a_decomposition;
  hence thesis by A1,Th3;
end;
