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(* 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>         *)
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Require Export Qsyntax.
Require Export Field_Theory_Q.
Require Export Q_ordered_field_properties.

(* Specifications: *)
Lemma Qpositive_in_Q_Archimedean_inf:forall qp:Qpositive, {z:Z | (Qpos qp)<=z /\ (z-(Qpos qp))<= Qone}.
Theorem Q_Archimedean_inf:forall q:Q, {z:Z | q<=z /\ (z-q)<= Qone}.
Definition up_Q q:= proj1_sig (Q_Archimedean_inf q).