Section QnatPred.
Definition Qnat := [qualify a x : rat | (x \is a Qint) && (0 <= x)].
Fact Qnat_key : pred_key Qnat. Proof. by []. Qed.
Canonical Qnat_keyed := KeyedQualifier Qnat_key.

Lemma Qnat_def x : (x \is a Qnat) = (x \is a Qint) && (0 <= x).