
theorem ApproxWithout:
  for T being with_equivalence naturally_generated non empty TopRelStr,
      A being Subset of T holds
    not A is 3rd_class
  proof
    let T be with_equivalence naturally_generated non empty TopRelStr,
      A be Subset of T;
A1: A is 3rd_class iff Cl Int A, Int Cl A are_c=-incomparable;
    LAp UAp A = UAp UAp A by ROUGHS_1:36 .= UAp A;
    hence thesis by ROUGHS_1:25,12,A1;
  end;
