Functional Scheme Z_to_Q_ind := Induction for Z_to_Q Sort Prop.

Lemma Z_to_Qplus_POS_NEG :
forall p1 p2 : positive,
Z_to_Q (Zpos p1 + Zneg p2) = Qplus (Z_to_Q (Zpos p1)) (Z_to_Q (Zneg p2)).