Introduce a Not type

This is a continuation of this discussion on the Intersection issue.

I have a different use case for the Not[...] type, but it is related to the original discussion. My usecase is to be able to tell the type checker that two types can never have an intersection. The specific case is for the phantom-types library where there are two types NonEmpty and Empty.

Currently there is no way to tell mypy that a variable can't both be NonEmpty and Empty, so this code passes without error:

from __future__ import annotations
from phantom.sized import NonEmpty, Empty

i: tuple[int, ...] = ()

assert isinstance(i, Empty)
assert isinstance(i, NonEmpty)

reveal_type(i)

The output shows that mypy interprets i as an intersection between tuple, Empty and NonEmpty:

intx.py:9: note: Revealed type is 'intx.<subclass of "tuple", "Empty", and "NonEmpty">'

Of course this code would error at runtime, but it would be preferable if this could be expressible so that type checkers can give an error here, similarly to how mypy gives errors for unreachable code.

A suggestion for how this could be expressed is to allow subclassing a Not type, so simplified the definitions of the two mentioned types would like this:

class NonEmpty:
    ...

class Empty(Not[NonEmpty]):
    ...

There are also other types in the library that would benefit from this like TZAware and TZNaive.

Edit: To clarify, I think that this type would be valuable even without an Intersection type which is why I opened a separate issue. This is because (as showed in the example) there already implicit intersections in mypy. I don't know how the other type checkers treats this.

Read the linked Intersection discussion and the phantom-types sized.py and datetime.py examples first. Then review the mypy behavior shown in the issue and compare how other type checkers handle implicit intersections. Done means a maintainer-approved design for expressing disjoint types and agreed checker behavior.