/* IOA */
  public String format_ioa() {
    if (var1().isIOASet() || var2().isIOASet()) return "Not valid for sets: " + format();
    Quantify.IOAQuantification quant1 = VarInfo.get_ioa_quantify(var1());
    Quantify.IOAQuantification quant2 = VarInfo.get_ioa_quantify(var2());

    return quant1.getQuantifierExp()
        + quant1.getVarIndexedString(0)
        + " "
        + "< "
        + quant2.getVarIndexedString(0)
        + quant1.getClosingExp();
  }
  /* IOA */
  public String format_ioa() {
    Quantify.IOAQuantification quant = VarInfo.get_ioa_quantify(var(), var());

    String result =
        quant.getQuantifierExp()
            + "("
            + quant.getMembershipRestriction(0)
            + " /\\ "
            + quant.getMembershipRestriction(1);

    // i \in X /\ j \in X => X[i] = X[j]

    result += ") => " + quant.getVarIndexedString(0) + " = " + quant.getVarIndexedString(1);
    return result + quant.getClosingExp();
  }