simpl; rewrite Q_to_R_Zero; ring.
(* Qpos *)
unfold Q_to_R, numerator, denominator, decode_Q, Qopp, fst, snd.
destruct (interp_non_zero p) as [p0 [q0 H]].
rewrite H.
repeat rewrite Ropp_Ropp_IZR; repeat rewrite <- INR_IZR_INZ.
field; auto.
(* Qneg *)
unfold Q_to_R, numerator, denominator, decode_Q, Qopp, fst, snd.
destruct (interp_non_zero p) as [p0 [q0 H]].
rewrite H.
repeat rewrite Ropp_Ropp_IZR; repeat rewrite <- INR_IZR_INZ.
field; auto.
Qed.

Lemma Q_to_Rlt: forall x y, Qlt x y -> Rlt (Q_to_R x) (Q_to_R y).