I think the problem here is that enumerating over a disjoint union of an
infinite set and a finite set will never reach the elements in the finite
set. There is this comment in the documentation of
DisjointUnionEnumeratedSets
Possible extensions: the current enumeration order is not suitable
> for unions of infinite enumerated sets (except possibly for the
> last one). One could add options to specify alternative enumeration
> orders (anti-diagonal, round robin, ...) to handle this case.
so the workaround is to first enumerate over the finite set and then the
infinite set, as the last enumerated set in the union will determine
whether the disjoint union is finite or not:
sage: DisjointUnionEnumeratedSets([NonNegativeIntegers(), Family('x')]) in
FiniteSets()
True
sage: DisjointUnionEnumeratedSets([Family('x'), NonNegativeIntegers()]) in
FiniteSets()
False
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