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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** [Qc] : A canonical representation of rational numbers. based on the setoid representation [Q]. *)
Record Qc : Set := Qcmake { this :> Q ; canon : Qred this = this }.
Declare Scope Qc_scope.
Delimit Scope Qc_scope with Qc.
Bind Scope Qc_scope with Qc.
Arguments Qcmake this%Q _.
Open Scope Qc_scope.
(** An alternative statement of [Qred q = q] via [Z.gcd] *)
(** Coercion from [Qc] to [Q] and equality *)
Hint Resolve Qc_is_canon : core.
(** [Q2Qc] : a conversion from [Q] to [Qc]. *)

Lemma Qred_involutive : forall q:Q, Qred (Qred q) = Qred q.