Definition Qplus' (p q : Q) := Qred (Qplus p q).
Definition Qmult' (p q : Q) := Qred (Qmult p q).

(* 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).
Add Morphism Qplus' : Qplus'_comp.