reserve T for TopSpace,
  B for Subset of T;

theorem Th6:
  B is semi-pre-open iff B = spInt B
proof
  hereby
    assume B is semi-pre-open;
    then B = B /\ (Cl Int B \/ Int Cl B) by XBOOLE_1:28;
    hence B = spInt B by XBOOLE_1:23;
  end;
  assume B = spInt B;
  then B = B /\ (Cl Int B \/ Int Cl B) by XBOOLE_1:23;
  hence thesis by XBOOLE_1:17;
end;
