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_SF.v,v 1.16.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/Ranalysis.ma".
41 include "Logic/Classical_Prop.ma".
44 Open Local Scope R_scope.
48 Set Implicit Arguments.
51 (*#*************************************************)
53 (* Each bounded subset of N has a maximal element *)
55 (*#*************************************************)
57 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Nbound.con" as definition.
59 inline procedural "cic:/Coq/Reals/RiemannInt_SF/IZN_var.con" as lemma.
61 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Nzorn.con" as lemma.
63 (*#******************************************)
67 (*#******************************************)
69 inline procedural "cic:/Coq/Reals/RiemannInt_SF/open_interval.con" as definition.
71 inline procedural "cic:/Coq/Reals/RiemannInt_SF/co_interval.con" as definition.
73 inline procedural "cic:/Coq/Reals/RiemannInt_SF/adapted_couple.con" as definition.
75 inline procedural "cic:/Coq/Reals/RiemannInt_SF/adapted_couple_opt.con" as definition.
77 inline procedural "cic:/Coq/Reals/RiemannInt_SF/is_subdivision.con" as definition.
79 inline procedural "cic:/Coq/Reals/RiemannInt_SF/IsStepFun.con" as definition.
81 (* Class of step functions *)
83 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun.ind".
85 inline procedural "cic:/Coq/Reals/RiemannInt_SF/subdivision.con" as definition.
87 inline procedural "cic:/Coq/Reals/RiemannInt_SF/subdivision_val.con" as definition.
89 inline procedural "cic:/Coq/Reals/RiemannInt_SF/Int_SF.con" as definition.
91 (* Integral of step functions *)
93 inline procedural "cic:/Coq/Reals/RiemannInt_SF/RiemannInt_SF.con" as definition.
95 (*#*******************************)
97 (* Properties of step functions *)
99 (*#*******************************)
101 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P1.con" as lemma.
103 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P2.con" as lemma.
105 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P3.con" as lemma.
107 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P4.con" as lemma.
109 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P5.con" as lemma.
111 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P6.con" as lemma.
113 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P7.con" as lemma.
115 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P8.con" as lemma.
117 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P9.con" as lemma.
119 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P10.con" as lemma.
121 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P11.con" as lemma.
123 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P12.con" as lemma.
125 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P13.con" as lemma.
127 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P14.con" as lemma.
129 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P15.con" as lemma.
131 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P16.con" as lemma.
133 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P17.con" as lemma.
135 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P18.con" as lemma.
137 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P19.con" as lemma.
139 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P20.con" as lemma.
141 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P21.con" as lemma.
143 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P22.con" as lemma.
145 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P23.con" as lemma.
147 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P24.con" as lemma.
149 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P25.con" as lemma.
151 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P26.con" as lemma.
153 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P27.con" as lemma.
155 (* The set of step functions on [a,b] is a vectorial space *)
157 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P28.con" as lemma.
159 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P29.con" as lemma.
161 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P30.con" as lemma.
163 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P31.con" as lemma.
165 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P32.con" as lemma.
167 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P33.con" as lemma.
169 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P34.con" as lemma.
171 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P35.con" as lemma.
173 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P36.con" as lemma.
175 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P37.con" as lemma.
177 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P38.con" as lemma.
179 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P39.con" as lemma.
181 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P40.con" as lemma.
183 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P41.con" as lemma.
185 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P42.con" as lemma.
187 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P43.con" as lemma.
189 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P44.con" as lemma.
191 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P45.con" as lemma.
193 inline procedural "cic:/Coq/Reals/RiemannInt_SF/StepFun_P46.con" as lemma.