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;
reserve X for non empty TopSpace,
  A1, A2 for Subset of X;

theorem
  A1,A2 are_weakly_separated iff A1`, A2` are_weakly_separated
proof
  A1, A1` constitute_a_decomposition & A2, A2` constitute_a_decomposition
  by Th5;
  hence thesis by Th15;
end;
