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).

Lemma Qplus'_correct : forall p q : Q, (Qplus' p q)==(Qplus p q).