(** [Qc] : A canonical representation of rational numbers.
   based on the setoid representation [Q]. *)

Record Qc : Set := Qcmake { this :> Q ; canon : Qred this = this }.(** [Qc] : A canonical representation of rational numbers.
   based on the setoid representation [Q]. *)

Record Qc : Set := Qcmake { this :> Q ; canon : Qred this = this }.(** [Qc] : A canonical representation of rational numbers.
   based on the setoid representation [Q]. *)

Record Qc : Set := Qcmake { this :> Q ; canon : Qred this = this }.(** [Qc] : A canonical representation of rational numbers.
   based on the setoid representation [Q]. *)

Record Qc : Set := Qcmake { this :> Q ; canon : Qred this = this }.

Lemma Qred_identity : forall q:Q, Z.gcd (Qnum q) (QDen q) = 1%Z -> Qred q = q.