from sympy.core.basic import Basic
from sympy.core.function import FunctionClass, Lambda
from sympy.multipledispatch import Dispatcher
from sympy.sets import FiniteSet, Intersection, Interval, Range, Union
from sympy.sets.fancysets import ImageSet, Integers, Naturals, Reals
from sympy.sets.sets import Complement, EmptySet, Set

FunctionUnion = ...
_set_function: Dispatcher

@_set_function.register(FunctionClass, Set)
def _(f, x) -> None: ...
@_set_function.register(FunctionUnion, FiniteSet)
def _(f, x) -> FiniteSet: ...
@_set_function.register(Lambda, Interval)
def _(f, x): ...
@_set_function.register(FunctionClass, Interval)
def _(f, x) -> FiniteSet | Interval | ImageSet: ...
@_set_function.register(FunctionUnion, Union)
def _(f, x) -> FiniteSet | Union: ...
@_set_function.register(FunctionUnion, Intersection)
def _(f, x) -> FiniteSet | Intersection | Union | Complement | ImageSet: ...
@_set_function.register(FunctionUnion, EmptySet)
def _(f, x): ...
@_set_function.register(FunctionUnion, Set)
def _(f, x) -> FiniteSet | ImageSet: ...
@_set_function.register(FunctionUnion, Range)
def _(f, self) -> FiniteSet | Basic | ImageSet | None: ...
@_set_function.register(FunctionUnion, Integers)
def _(f, self) -> FiniteSet | ImageSet | None: ...
@_set_function.register(FunctionUnion, Naturals)
def _(f, self) -> Range | None: ...
@_set_function.register(FunctionUnion, Reals)
def _(f, self) -> None: ...