Add Morphism Qred with signature (Qeq ==> Qeq) as Qred_comp.Definition Qplus' (p q : Q) := Qred (Qplus p q).Definition Qmult' (p q : Q) := Qred (Qmult p q).Definition Qminus' x y := Qred (Qminus x y).

(* Specifications: *)
Lemma Qplus'_correct : forall p q : Q, (Qplus' p q)==(Qplus p q).
Lemma Qmult'_correct : forall p q : Q, (Qmult' p q)==(Qmult p q).
Lemma Qminus'_correct : forall p q : Q, (Qminus' p q)==(Qminus p q).