1 (**************************************************************************)
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 *)
13 (**************************************************************************)
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: RiemannInt.v,v 1.18.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
35 include "Reals/Rfunctions.ma".
37 include "Reals/SeqSeries.ma".
39 include "Reals/Ranalysis.ma".
41 include "Reals/Rbase.ma".
43 include "Reals/RiemannInt_SF.ma".
45 include "Logic/Classical_Prop.ma".
47 include "Logic/Classical_Pred_Type.ma".
49 include "Arith/Max.ma".
52 Open Local Scope R_scope.
56 Set Implicit Arguments.
59 (*#*******************************************)
61 (* Riemann's Integral *)
63 (*#*******************************************)
65 inline procedural "cic:/Coq/Reals/RiemannInt/Riemann_integrable.con" as definition.
67 inline procedural "cic:/Coq/Reals/RiemannInt/phi_sequence.con" as definition.
69 inline procedural "cic:/Coq/Reals/RiemannInt/phi_sequence_prop.con" as lemma.
71 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P1.con" as lemma.
73 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P2.con" as lemma.
75 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P3.con" as lemma.
77 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_exists.con" as lemma.
79 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P4.con" as lemma.
81 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN_pos.con" as lemma.
83 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN.con" as definition.
85 inline procedural "cic:/Coq/Reals/RiemannInt/RinvN_cv.con" as lemma.
89 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt.con" as definition.
91 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P5.con" as lemma.
93 (*#*************************************)
95 (* C\176\([a,b]) is included in L1([a,b]) *)
97 (*#*************************************)
99 inline procedural "cic:/Coq/Reals/RiemannInt/maxN.con" as lemma.
101 inline procedural "cic:/Coq/Reals/RiemannInt/SubEquiN.con" as definition.
103 inline procedural "cic:/Coq/Reals/RiemannInt/max_N.con" as definition.
105 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui.con" as definition.
107 inline procedural "cic:/Coq/Reals/RiemannInt/Heine_cor1.con" as lemma.
109 inline procedural "cic:/Coq/Reals/RiemannInt/Heine_cor2.con" as lemma.
111 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P1.con" as lemma.
113 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P2.con" as lemma.
115 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P3.con" as lemma.
117 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P4.con" as lemma.
119 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P5.con" as lemma.
121 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P6.con" as lemma.
123 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P7.con" as lemma.
125 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P8.con" as lemma.
127 inline procedural "cic:/Coq/Reals/RiemannInt/SubEqui_P9.con" as lemma.
129 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P6.con" as lemma.
131 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P7.con" as lemma.
133 inline procedural "cic:/Coq/Reals/RiemannInt/continuity_implies_RiemannInt.con" as lemma.
135 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P8.con" as lemma.
137 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P9.con" as lemma.
139 inline procedural "cic:/Coq/Reals/RiemannInt/Req_EM_T.con" as lemma.
141 (* L1([a,b]) is a vectorial space *)
143 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P10.con" as lemma.
145 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P11.con" as lemma.
147 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P12.con" as lemma.
149 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P13.con" as lemma.
151 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P14.con" as lemma.
153 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P15.con" as lemma.
155 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P16.con" as lemma.
157 inline procedural "cic:/Coq/Reals/RiemannInt/Rle_cv_lim.con" as lemma.
159 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P17.con" as lemma.
161 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P18.con" as lemma.
163 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P19.con" as lemma.
165 inline procedural "cic:/Coq/Reals/RiemannInt/FTC_P1.con" as lemma.
167 inline procedural "cic:/Coq/Reals/RiemannInt/primitive.con" as definition.
169 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P20.con" as lemma.
171 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P21.con" as lemma.
173 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P22.con" as lemma.
175 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P23.con" as lemma.
177 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P24.con" as lemma.
179 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P25.con" as lemma.
181 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P26.con" as lemma.
183 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P27.con" as lemma.
185 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P28.con" as lemma.
187 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P29.con" as lemma.
189 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P30.con" as lemma.
191 inline procedural "cic:/Coq/Reals/RiemannInt/C1_fun.ind".
193 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P31.con" as lemma.
195 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P32.con" as lemma.
197 inline procedural "cic:/Coq/Reals/RiemannInt/RiemannInt_P33.con" as lemma.
199 inline procedural "cic:/Coq/Reals/RiemannInt/FTC_Riemann.con" as lemma.