Does DataFrame.index.empty imply DataFrame.empty?
yes, if index of DataFrame is empty it will always satisfies condition of DataFrame.empty
For e.g

DataFrame.empty = True

works in both condition for index as well as for columns.
Hence if you want to check any of these are empty then you can go with

DataFrame.empty

else need to be specific

DataFrame.index.empty
If I have a DataFrame, df, for which df.index.empy is True, will this ALWAYS imply that df.empty is also True?
My intend is to test only df.index.empy when I need to test both conditions (lazy programming style).