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

Theorem Qred_compare: forall x y,
Qcompare x y = Qcompare (Qred x) (Qred y).