Index.intersection does not return correct sub type

[StefanBrand]

Describe the bug
When I form the intersection of two pd.DatetimeIndex, the return type is Index. This leads to problems with index entries: mypy complains about intersection[0].date().

To Reproduce

1. Minimal example

import pandas as pd
intersection = pd.DatetimeIndex().intersection(pd.DatetimeIndex)

reveal_type(intersection)  # Index
reveal_type(intersection[0])  # "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex"

2. mypy

3. error message

agri_data/utils.py:96: error: Item "str" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "bytes" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "date" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "timedelta" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "datetime64" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "timedelta64" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "bool" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "int" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "float" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "Timedelta" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]
agri_data/utils.py:96: error: Item "complex" of "str | bytes | date | datetime | timedelta | datetime64 | timedelta64 | bool | int | float | Timestamp | Timedelta | complex" has no attribute "date"  [union-attr]

4. Expected type: reveal_type(intersection[0]) # Timestamp

Please complete the following information:

• OS: Ubuntu
• OS Version: bullseye
• python version: 3.11.1
• version of type checker: 1.2.0
• version of installed pandas-stubs: 2.0.2.230605

Additional context
Possibly related: #723

[Dr-Irv]

Thanks for the report.

Need to add intersection() to pandas-stubs/core/indexes/datetimes.pyi

[teacherc]

take

[teacherc]

@Dr-Irv Can I work on this issue? (it wasn't assigned to me automatically with 'take')

[teacherc]

@Dr-Irv Hello there! I'm new to open source. I just did a pull request. Let me know if you have any changes/questions. Thank you.