An enum.Flag subclass that supports all frozenset operations.

set_like_flag.py

from enum import Flag

class SetLikeFlag(Flag):
    """Flag that additionally supports all frozenset operations."""
    def __repr__(self):
        """Only show the flag names, not values."""
        return super().__repr__().split(':', 1)[0] + '>'
    def __sub__(self, other):
        """Asymmetric difference of this set of flags with the other."""
        if not isinstance(other, type(self)):
            return NotImplemented
        return self & ~other
    def __le__(self, other):
        """Whether this set of flags is a subset of the other."""
        if not isinstance(other, type(self)):
            return NotImplemented
        return (self & other) == self
    def __lt__(self, other):
        """Whether this set of flags is a proper subset of the other."""
        if not isinstance(other, type(self)):
            return NotImplemented
        return self <= other and self != other
    def __ge__(self, other):
        """Whether this set of flags is a superset of the other."""
        return other <= self
    def __gt__(self, other):
        """Whether this set of flags is a proper superset of the other."""
        return other < self

test_set_like_flag.py

from enum import auto
from set_like_flag import SetLikeFlag

class U(SetLikeFlag):
    """Definition of the universe."""
    A = auto()
    B = auto()
    C = auto()
    D = auto()

def test_set_like_flag():
    # operator precedence dictates these parentheses
    assert (U.A|U.B|U.C) - (U.B|U.C|U.D) == U.A, "incorrect asymmetric difference"
    assert U.A|U.B <= U.A|U.B|U.C, "should be subset"
    assert U.A|U.B < U.A|U.B|U.C, "should be proper subset"
    assert U.A|U.B|U.C <= U.A|U.B|U.C, "should be subset"
    assert not (U.A|U.B|U.C < U.A|U.B|U.C), "shouldn't be proper subset"
    assert not (U.A|U.B|U.D <= U.A|U.B|U.C), "shouldn't be subset"
    assert U.A|U.B|U.C >= U.A|U.B, "should be superset"
    assert U.A|U.B|U.C > U.A|U.B, "should be proper superset"
    assert U.A|U.B|U.C >= U.A|U.B|U.C, "should be superset"
    assert not (U.A|U.B|U.C > U.A|U.B|U.C), "shouldn't be proper superset"
    assert not (U.A|U.B|U.C >= U.A|U.B|U.D), "shouldn't be superset"