(************************************************************************)
(* Copyright 2006 Milad Niqui                                           *)
(* This file is distributed under the terms of the                      *)
(* GNU Lesser General Public License Version 2.1                        *)
(* A copy of the license can be found at                                *)
(*                  <http://www.gnu.org/licenses/lgpl-2.1.html>         *)
(************************************************************************)
Require Export Qsyntax.
Require Export Field_Theory_Q.
Require Export Q_ordered_field_properties.
Definition up_Q q:= proj1_sig (Q_Archimedean_inf q).
Definition up_Q_property q := proj2_sig (Q_Archimedean_inf q):  q <= (up_Q q) /\ (up_Q q) - q <= Qone.

Lemma Q_Archimedean_nat_inf:forall q:Q, {n:nat | q<=n }.