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

Lemma Qred_lt q q' : Qred q < Qred q' <-> q < q'.