proposition: Lemma Q_to_Ropp: forall x, Q_to_R (Qopp x) = Ropp (Q_to_R x).
proof: Proof. intros [ |p|p]. simpl; rewrite Q_to_R_Zero; ring. 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. 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.
imports: QArithSternBrocot(Q_ordered_field_properties) QArithSternBrocot(R_addenda) Coq(Raxioms) Coq(RIneq)