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 constitute_a_decomposition implies (A1,A2 are_weakly_separated
  iff A1,A2 are_separated)
by TSEP_1:46;
