Functional Scheme Qpositive_plus_ind := Induction for Qpositive_plus Sort Prop.

Lemma Qmult_Z_nR :
forall (a : Z) (p : Qpositive),
Qmult (Z_to_Q a) (Qpos (nR p)) =
Qplus (Qmult (Z_to_Q a) (Qpos p)) (Z_to_Q a).