(** We define the injection from Q into R *)

Definition Q_to_R (q:Q) : R := ((IZR (numerator q))/(IZR (denominator q)))%R.

Lemma Q_to_Rdiv: forall x y, ~(y=Zero) -> Q_to_R (Qdiv x y) = (Rdiv (Q_to_R x) (Q_to_R y)).