code: def test_add_time_index_through_woodwork_different_type(dates_df):
      dates_df.ww.init(
          name="dates_table",
          index="backwards_order",
          time_index="dates_backwards",
      )
      es = EntitySet("es")
  
      es.add_dataframe(
          dates_df,
          secondary_time_index={
              "repeating_dates": ["random_order", "special"]
          },
      )
  
      assert dates_df.ww.metadata["secondary_time_index"] == {
          "repeating_dates": [
              "random_order",
              "special",
              "repeating_dates",
          ],
      }
      assert es.time_type == Datetime
  
      assert es._check_uniform_time_index(es["dates_table"]) is None
  
      dates_df.ww.set_time_index("random_order")
      assert dates_df.ww.time_index == "random_order"
  
      error = "dates_table time index is numeric type which differs from other entityset time indexes"
      with pytest.raises(TypeError, match=error):
          es._check_uniform_time_index(es["dates_table"])
  
imports: from datetime import datetime
  import numpy
  import pandas
  import pytest
  from woodwork.exceptions import TypeConversionError
  from woodwork.logical_types import Boolean, Categorical, Datetime, Double, Integer, NaturalLanguage
  from featuretools.entityset.entityset import LTI_COLUMN_NAME, EntitySet
  from featuretools.tests.testing_utils import to_pandas
  from featuretools.utils.gen_utils import Library, import_or_none, is_instance
label_desc: Use image node_id 17 for calling a global function with example usage: test_add_time_index_through_woodwork_different_type(dates_df) without return types