Functional Scheme Z_to_Q_ind := Induction for Z_to_Q Sort Prop.

Lemma Qmult_Z_plus_Z_dL :
forall (a b : Z) (p : Qpositive),
Qplus (Qmult (Z_to_Q a) (Qpos (dL p))) (Z_to_Q b) =
Qmult (Qplus (Qmult (Z_to_Q (a + b)) (Qpos p)) (Z_to_Q b))
(Qinv (Qplus (Qpos p) Qone)).