]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/procedural/Coq/Reals/NewtonInt.mma
Stuff moved from old Matita.
[helm.git] / matita / matita / contribs / procedural / Coq / Reals / NewtonInt.mma
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: NewtonInt.v,v 1.11.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)
34
35 include "Reals/Rbase.ma".
36
37 include "Reals/Rfunctions.ma".
38
39 include "Reals/SeqSeries.ma".
40
41 include "Reals/Rtrigo.ma".
42
43 include "Reals/Ranalysis.ma".
44
45 (* UNEXPORTED
46 Open Local Scope R_scope.
47 *)
48
49 (*#******************************************)
50
51 (*            Newton's Integral            *)
52
53 (*#******************************************)
54
55 inline procedural "cic:/Coq/Reals/NewtonInt/Newton_integrable.con" as definition.
56
57 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt.con" as definition.
58
59 (* If f is differentiable, then f' is Newton integrable (Tautology ?) *)
60
61 inline procedural "cic:/Coq/Reals/NewtonInt/FTCN_step1.con" as lemma.
62
63 (* By definition, we have the Fondamental Theorem of Calculus *)
64
65 inline procedural "cic:/Coq/Reals/NewtonInt/FTC_Newton.con" as lemma.
66
67 (* $\int_a^a f$ exists forall a:R and f:R->R *)
68
69 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P1.con" as lemma.
70
71 (* $\int_a^a f = 0$ *)
72
73 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P2.con" as lemma.
74
75 (* If $\int_a^b f$ exists, then $\int_b^a f$ exists too *)
76
77 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P3.con" as lemma.
78
79 (* $\int_a^b f = -\int_b^a f$ *)
80
81 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P4.con" as lemma.
82
83 (* The set of Newton integrable functions is a vectorial space *)
84
85 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P5.con" as lemma.
86
87 (*#*********)
88
89 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P1.con" as lemma.
90
91 (* $\int_a^b \lambda f + g = \lambda \int_a^b f + \int_a^b f *)
92
93 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P6.con" as lemma.
94
95 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P2.con" as lemma.
96
97 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P3.con" as lemma.
98
99 inline procedural "cic:/Coq/Reals/NewtonInt/antiderivative_P4.con" as lemma.
100
101 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P7.con" as lemma.
102
103 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P8.con" as lemma.
104
105 (* Chasles' relation *)
106
107 inline procedural "cic:/Coq/Reals/NewtonInt/NewtonInt_P9.con" as lemma.
108