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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals".
21 (* $Id: CReals.v,v 1.2 2004/04/05 11:35:38 lcf Exp $ *)
23 (*#* printing Lim %\ensuremath{\lim}% *)
25 include "algebra/COrdCauchy.ma".
27 (*#* * Definition of the notion of reals
28 The reals are defined as a Cauchy-closed Archimedean constructive
29 ordered field in which we have a maximum function. The maximum
30 function is definable, using countable choice, but in a rather tricky
31 way. Cauchy completeness is stated by assuming a function [lim]
32 that returns a real number for every Cauchy sequence together with a
33 proof that this number is the limit.
38 inline "cic:/CoRN/reals/CReals/is_CReals.ind".
40 inline "cic:/CoRN/reals/CReals/CReals.ind".
42 coercion cic:/matita/CoRN-Decl/reals/CReals/crl_crr.con 0 (* compounds *).
46 inline "cic:/CoRN/reals/CReals/Lim.con".
49 Implicit Arguments Lim [IR].