Section QintPred.
Definition Qint := [qualify a x : rat | denq x == 1].
Fact Qint_key : pred_key Qint. Proof. by []. Qed.
Canonical Qint_keyed := KeyedQualifier Qint_key.

Lemma numqK : {in Qint, cancel (fun x => numq x) intr}.
Fact Qint_subring_closed : subring_closed Qint.