Add Morphism Qplus' with signature (Qeq ==> Qeq ==> Qeq) as Qplus'_comp.Add Morphism Qmult' with signature (Qeq ==> Qeq ==> Qeq) as Qmult'_comp.Add Morphism Qminus' with signature (Qeq ==> Qeq ==> Qeq) as Qminus'_comp.

Lemma Qred_opp: forall q, Qred (-q) = - (Qred q).