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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 *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: PartSum.v,v 1.11.2.1 2004/07/16 19:31:11 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/Rseries.ma".
41 include "Reals/Rcomplete.ma".
43 include "Arith/Max.ma".
46 Open Local Scope R_scope.
49 inline procedural "cic:/Coq/Reals/PartSum/tech1.con" as lemma.
51 (* Chasles' relation *)
53 inline procedural "cic:/Coq/Reals/PartSum/tech2.con" as lemma.
55 (* Sum of geometric sequences *)
57 inline procedural "cic:/Coq/Reals/PartSum/tech3.con" as lemma.
59 inline procedural "cic:/Coq/Reals/PartSum/tech4.con" as lemma.
61 inline procedural "cic:/Coq/Reals/PartSum/tech5.con" as lemma.
63 inline procedural "cic:/Coq/Reals/PartSum/tech6.con" as lemma.
65 inline procedural "cic:/Coq/Reals/PartSum/tech7.con" as lemma.
67 inline procedural "cic:/Coq/Reals/PartSum/tech11.con" as lemma.
69 inline procedural "cic:/Coq/Reals/PartSum/tech12.con" as lemma.
71 inline procedural "cic:/Coq/Reals/PartSum/scal_sum.con" as lemma.
73 inline procedural "cic:/Coq/Reals/PartSum/decomp_sum.con" as lemma.
75 inline procedural "cic:/Coq/Reals/PartSum/plus_sum.con" as lemma.
77 inline procedural "cic:/Coq/Reals/PartSum/sum_eq.con" as lemma.
79 (* Unicity of the limit defined by convergent series *)
81 inline procedural "cic:/Coq/Reals/PartSum/uniqueness_sum.con" as lemma.
83 inline procedural "cic:/Coq/Reals/PartSum/minus_sum.con" as lemma.
85 inline procedural "cic:/Coq/Reals/PartSum/sum_decomposition.con" as lemma.
87 inline procedural "cic:/Coq/Reals/PartSum/sum_Rle.con" as lemma.
89 inline procedural "cic:/Coq/Reals/PartSum/Rsum_abs.con" as lemma.
91 inline procedural "cic:/Coq/Reals/PartSum/sum_cte.con" as lemma.
95 inline procedural "cic:/Coq/Reals/PartSum/sum_growing.con" as lemma.
99 inline procedural "cic:/Coq/Reals/PartSum/Rabs_triang_gen.con" as lemma.
103 inline procedural "cic:/Coq/Reals/PartSum/cond_pos_sum.con" as lemma.
105 (* Cauchy's criterion for series *)
107 inline procedural "cic:/Coq/Reals/PartSum/Cauchy_crit_series.con" as definition.
109 (* If (|An|) satisfies the Cauchy's criterion for series, then (An) too *)
111 inline procedural "cic:/Coq/Reals/PartSum/cauchy_abs.con" as lemma.
115 inline procedural "cic:/Coq/Reals/PartSum/cv_cauchy_1.con" as lemma.
117 inline procedural "cic:/Coq/Reals/PartSum/cv_cauchy_2.con" as lemma.
121 inline procedural "cic:/Coq/Reals/PartSum/sum_eq_R0.con" as lemma.
123 inline procedural "cic:/Coq/Reals/PartSum/SP.con" as definition.
127 inline procedural "cic:/Coq/Reals/PartSum/sum_incr.con" as lemma.
131 inline procedural "cic:/Coq/Reals/PartSum/sum_cv_maj.con" as lemma.