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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.
Definition Qmax p q := if Q_le_lt_dec p q then q else p.
Definition Qmin p q := if Q_le_lt_dec p q then p else q.
Definition Qmax4 q1 q2 q3 q4 := Qmax (Qmax q1 q2) (Qmax q3 q4).
Definition Qmin4 q1 q2 q3 q4 := Qmin (Qmin q1 q2) (Qmin q3 q4).

Lemma Qlt_Qmin_upper_bound: forall p q1 q2 : Q, p < Qmin q1 q2 -> p < q1 /\ p < q2.