def apply(n, k, s0=None, B=None):
if s0 is None:
x = Symbol.x(shape=(oo, ), dtype=dtype.integer, finite=True)
s0 = Symbol.s0(definition=UNION[x[:k]:Stirling.conditionset(n, k, x)](
x[:k].set_comprehension().set))
if B is None:
e = Symbol.e(**s0.element_type.dict)
B = Symbol.B(definition=UNION[e:s0]({e | {n.set}}))
return Equality(abs(s0), abs(B))
def apply(n, k, s2=None, B=None):
if s2 is None:
x = Symbol.x(shape=(oo, ), dtype=dtype.integer, finite=True)
s2 = Symbol.s2(
definition=UNION[x[:k + 1]:Stirling.conditionset(n + 1, k + 1, x)](
x[:k + 1].set_comprehension().set))
e = Symbol.e(**s2.element_type.dict)
if B is None:
x = s2.definition.variable.base
s0 = Symbol.s0(definition=UNION[x[:k]:Stirling.conditionset(n, k, x)](
x[:k].set_comprehension().set))
B = Symbol.B(definition=UNION[e:s0]({e | {n.set}}))
return Equality(conditionset(e, Contains({n}, e), s2), B)
