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