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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: PSeries_reg.v,v 1.12.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/SeqSeries.ma".
41 include "Reals/Ranalysis1.ma".
43 include "Arith/Max.ma".
45 include "Arith/Even.ma".
48 Open Local Scope R_scope.
51 inline procedural "cic:/Coq/Reals/PSeries_reg/Boule.con" as definition.
53 (* Uniform convergence *)
55 inline procedural "cic:/Coq/Reals/PSeries_reg/CVU.con" as definition.
57 (* Normal convergence *)
59 inline procedural "cic:/Coq/Reals/PSeries_reg/CVN_r.con" as definition.
61 inline procedural "cic:/Coq/Reals/PSeries_reg/CVN_R.con" as definition.
63 inline procedural "cic:/Coq/Reals/PSeries_reg/SFL.con" as definition.
65 (* In a complete space, normal convergence implies uniform convergence *)
67 inline procedural "cic:/Coq/Reals/PSeries_reg/CVN_CVU.con" as lemma.
69 (* Each limit of a sequence of functions which converges uniformly is continue *)
71 inline procedural "cic:/Coq/Reals/PSeries_reg/CVU_continuity.con" as lemma.
75 inline procedural "cic:/Coq/Reals/PSeries_reg/continuity_pt_finite_SF.con" as lemma.
77 (* Continuity and normal convergence *)
79 inline procedural "cic:/Coq/Reals/PSeries_reg/SFL_continuity_pt.con" as lemma.
81 inline procedural "cic:/Coq/Reals/PSeries_reg/SFL_continuity.con" as lemma.
83 (* As R is complete, normal convergence implies that (fn) is simply-uniformly convergent *)
85 inline procedural "cic:/Coq/Reals/PSeries_reg/CVN_R_CVS.con" as lemma.