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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 (* This file was automatically generated: do not edit *********************)
16
17 include "Coq.ma".
18
19 (*#***********************************************************************)
20
21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
22
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
24
25 (*   \VV/  **************************************************************)
26
27 (*    //   *      This file is distributed under the terms of the       *)
28
29 (*         *       GNU Lesser General Public License Version 2.1        *)
30
31 (*#***********************************************************************)
32
33 (*i $Id: SeqProp.v,v 1.13.2.1 2004/07/16 19:31:15 herbelin Exp $ i*)
34
35 include "Reals/Rbase.ma".
36
37 include "Reals/Rfunctions.ma".
38
39 include "Reals/Rseries.ma".
40
41 include "Logic/Classical.ma".
42
43 include "Arith/Max.ma".
44
45 (* UNEXPORTED
46 Open Local Scope R_scope.
47 *)
48
49 inline procedural "cic:/Coq/Reals/SeqProp/Un_decreasing.con" as definition.
50
51 inline procedural "cic:/Coq/Reals/SeqProp/opp_seq.con" as definition.
52
53 inline procedural "cic:/Coq/Reals/SeqProp/has_ub.con" as definition.
54
55 inline procedural "cic:/Coq/Reals/SeqProp/has_lb.con" as definition.
56
57 (*#*********)
58
59 inline procedural "cic:/Coq/Reals/SeqProp/growing_cv.con" as lemma.
60
61 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_growing.con" as lemma.
62
63 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_cv.con" as lemma.
64
65 (*#**********)
66
67 inline procedural "cic:/Coq/Reals/SeqProp/maj_sup.con" as lemma.
68
69 (*#*********)
70
71 inline procedural "cic:/Coq/Reals/SeqProp/min_inf.con" as lemma.
72
73 inline procedural "cic:/Coq/Reals/SeqProp/majorant.con" as definition.
74
75 inline procedural "cic:/Coq/Reals/SeqProp/minorant.con" as definition.
76
77 inline procedural "cic:/Coq/Reals/SeqProp/maj_ss.con" as lemma.
78
79 inline procedural "cic:/Coq/Reals/SeqProp/min_ss.con" as lemma.
80
81 inline procedural "cic:/Coq/Reals/SeqProp/sequence_majorant.con" as definition.
82
83 inline procedural "cic:/Coq/Reals/SeqProp/sequence_minorant.con" as definition.
84
85 inline procedural "cic:/Coq/Reals/SeqProp/Wn_decreasing.con" as lemma.
86
87 inline procedural "cic:/Coq/Reals/SeqProp/Vn_growing.con" as lemma.
88
89 (*#*********)
90
91 inline procedural "cic:/Coq/Reals/SeqProp/Vn_Un_Wn_order.con" as lemma.
92
93 inline procedural "cic:/Coq/Reals/SeqProp/min_maj.con" as lemma.
94
95 inline procedural "cic:/Coq/Reals/SeqProp/maj_min.con" as lemma.
96
97 (*#*********)
98
99 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_maj.con" as lemma.
100
101 (*#*********)
102
103 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_opp.con" as lemma.
104
105 (*#*********)
106
107 inline procedural "cic:/Coq/Reals/SeqProp/cauchy_min.con" as lemma.
108
109 (*#*********)
110
111 inline procedural "cic:/Coq/Reals/SeqProp/maj_cv.con" as lemma.
112
113 (*#*********)
114
115 inline procedural "cic:/Coq/Reals/SeqProp/min_cv.con" as lemma.
116
117 inline procedural "cic:/Coq/Reals/SeqProp/cond_eq.con" as lemma.
118
119 inline procedural "cic:/Coq/Reals/SeqProp/not_Rlt.con" as lemma.
120
121 (*#*********)
122
123 inline procedural "cic:/Coq/Reals/SeqProp/approx_maj.con" as lemma.
124
125 (*#*********)
126
127 inline procedural "cic:/Coq/Reals/SeqProp/approx_min.con" as lemma.
128
129 (* Unicity of limit for convergent sequences *)
130
131 inline procedural "cic:/Coq/Reals/SeqProp/UL_sequence.con" as lemma.
132
133 (*#*********)
134
135 inline procedural "cic:/Coq/Reals/SeqProp/CV_plus.con" as lemma.
136
137 (*#*********)
138
139 inline procedural "cic:/Coq/Reals/SeqProp/cv_cvabs.con" as lemma.
140
141 (*#*********)
142
143 inline procedural "cic:/Coq/Reals/SeqProp/CV_Cauchy.con" as lemma.
144
145 (*#*********)
146
147 inline procedural "cic:/Coq/Reals/SeqProp/maj_by_pos.con" as lemma.
148
149 (*#*********)
150
151 inline procedural "cic:/Coq/Reals/SeqProp/CV_mult.con" as lemma.
152
153 inline procedural "cic:/Coq/Reals/SeqProp/tech9.con" as lemma.
154
155 inline procedural "cic:/Coq/Reals/SeqProp/tech10.con" as lemma.
156
157 inline procedural "cic:/Coq/Reals/SeqProp/tech13.con" as lemma.
158
159 (*#*********)
160
161 inline procedural "cic:/Coq/Reals/SeqProp/growing_ineq.con" as lemma.
162
163 (* Un->l => (-Un) -> (-l) *)
164
165 inline procedural "cic:/Coq/Reals/SeqProp/CV_opp.con" as lemma.
166
167 (*#*********)
168
169 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_ineq.con" as lemma.
170
171 (*#*********)
172
173 inline procedural "cic:/Coq/Reals/SeqProp/CV_minus.con" as lemma.
174
175 (* Un -> +oo *)
176
177 inline procedural "cic:/Coq/Reals/SeqProp/cv_infty.con" as definition.
178
179 (* Un -> +oo => /Un -> O *)
180
181 inline procedural "cic:/Coq/Reals/SeqProp/cv_infty_cv_R0.con" as lemma.
182
183 (*#*********)
184
185 inline procedural "cic:/Coq/Reals/SeqProp/decreasing_prop.con" as lemma.
186
187 (* |x|^n/n! -> 0 *)
188
189 inline procedural "cic:/Coq/Reals/SeqProp/cv_speed_pow_fact.con" as lemma.
190