How can I find records by "count" of association using rails and mongoid?

With these models:

class Week
  has_many :proofs
end
class Proof
  belongs_to :week
end

I want to do something like:

Week.where(:proof.count.gt => 0)

To find only weeks that have multiple proofs.

There is one answer that seems to address this:

Can rails scopes filter on the number of associated classes for a given field

But in this example, there is no such attribute as proof_ids in Week since the ids are stored with the proofs. This does not work for example:

Week.where(:proof_ids.gt => 0)

How is this query possible? Conceptually simple but I can't figure out how to do this with mongo or mongoid.

Similarly, I'd like to order by the number of proofs for example like:

Week.desc(:proofs.size)

But this also does not work.

I do realize that a counter-cache is an option to both my specific questions but I'd also like to be able to do the query.

Thanks in advance for any help.