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19 (* $Id: CReals.v,v 1.2 2004/04/05 11:35:38 lcf Exp $ *)
21 (*#* printing Lim %\ensuremath{\lim}% *)
23 include "algebra/COrdCauchy.ma".
25 (*#* * Definition of the notion of reals
26 The reals are defined as a Cauchy-closed Archimedean constructive
27 ordered field in which we have a maximum function. The maximum
28 function is definable, using countable choice, but in a rather tricky
29 way. Cauchy completeness is stated by assuming a function [lim]
30 that returns a real number for every Cauchy sequence together with a
31 proof that this number is the limit.
36 inline procedural "cic:/CoRN/reals/CReals/is_CReals.ind".
38 inline procedural "cic:/CoRN/reals/CReals/CReals.ind".
41 cic:/matita/CoRN-Procedural/reals/CReals/crl_crr.con
46 inline procedural "cic:/CoRN/reals/CReals/Lim.con" as definition.
49 Implicit Arguments Lim [IR].