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: Rpower.v,v 1.17.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
35 (*i Due to L.Thery i*)
37 (*#***********************************************************)
39 (* Definitions of log and Rpower : R->R->R; main properties *)
41 (*#***********************************************************)
43 include "Reals/Rbase.ma".
45 include "Reals/Rfunctions.ma".
47 include "Reals/SeqSeries.ma".
49 include "Reals/Rtrigo.ma".
51 include "Reals/Ranalysis1.ma".
53 include "Reals/Exp_prop.ma".
55 include "Reals/Rsqrt_def.ma".
57 include "Reals/R_sqrt.ma".
59 include "Reals/MVT.ma".
61 include "Reals/Ranalysis4.ma".
64 Open Local Scope R_scope.
67 inline procedural "cic:/Coq/Reals/Rpower/P_Rmin.con" as lemma.
69 inline procedural "cic:/Coq/Reals/Rpower/exp_le_3.con" as lemma.
71 (*#*****************************************************************)
73 (* Properties of Exp *)
75 (*#*****************************************************************)
77 inline procedural "cic:/Coq/Reals/Rpower/exp_increasing.con" as theorem.
79 inline procedural "cic:/Coq/Reals/Rpower/exp_lt_inv.con" as theorem.
81 inline procedural "cic:/Coq/Reals/Rpower/exp_ineq1.con" as lemma.
83 inline procedural "cic:/Coq/Reals/Rpower/ln_exists1.con" as lemma.
87 inline procedural "cic:/Coq/Reals/Rpower/ln_exists.con" as lemma.
89 (* Definition of log R+* -> R *)
91 inline procedural "cic:/Coq/Reals/Rpower/Rln.con" as definition.
95 inline procedural "cic:/Coq/Reals/Rpower/ln.con" as definition.
97 inline procedural "cic:/Coq/Reals/Rpower/exp_ln.con" as lemma.
99 inline procedural "cic:/Coq/Reals/Rpower/exp_inv.con" as theorem.
101 inline procedural "cic:/Coq/Reals/Rpower/exp_Ropp.con" as theorem.
103 (*#*****************************************************************)
105 (* Properties of Ln *)
107 (*#*****************************************************************)
109 inline procedural "cic:/Coq/Reals/Rpower/ln_increasing.con" as theorem.
111 inline procedural "cic:/Coq/Reals/Rpower/ln_exp.con" as theorem.
113 inline procedural "cic:/Coq/Reals/Rpower/ln_1.con" as theorem.
115 inline procedural "cic:/Coq/Reals/Rpower/ln_lt_inv.con" as theorem.
117 inline procedural "cic:/Coq/Reals/Rpower/ln_inv.con" as theorem.
119 inline procedural "cic:/Coq/Reals/Rpower/ln_mult.con" as theorem.
121 inline procedural "cic:/Coq/Reals/Rpower/ln_Rinv.con" as theorem.
123 inline procedural "cic:/Coq/Reals/Rpower/ln_continue.con" as theorem.
125 (*#*****************************************************************)
127 (* Definition of Rpower *)
129 (*#*****************************************************************)
131 inline procedural "cic:/Coq/Reals/Rpower/Rpower.con" as definition.
134 Infix Local "^R" := Rpower (at level 30, right associativity) : R_scope.
137 (*#*****************************************************************)
139 (* Properties of Rpower *)
141 (*#*****************************************************************)
143 inline procedural "cic:/Coq/Reals/Rpower/Rpower_plus.con" as theorem.
145 inline procedural "cic:/Coq/Reals/Rpower/Rpower_mult.con" as theorem.
147 inline procedural "cic:/Coq/Reals/Rpower/Rpower_O.con" as theorem.
149 inline procedural "cic:/Coq/Reals/Rpower/Rpower_1.con" as theorem.
151 inline procedural "cic:/Coq/Reals/Rpower/Rpower_pow.con" as theorem.
153 inline procedural "cic:/Coq/Reals/Rpower/Rpower_lt.con" as theorem.
155 inline procedural "cic:/Coq/Reals/Rpower/Rpower_sqrt.con" as theorem.
157 inline procedural "cic:/Coq/Reals/Rpower/Rpower_Ropp.con" as theorem.
159 inline procedural "cic:/Coq/Reals/Rpower/Rle_Rpower.con" as theorem.
161 inline procedural "cic:/Coq/Reals/Rpower/ln_lt_2.con" as theorem.
163 (*#*************************************)
165 (* Differentiability of Ln and Rpower *)
167 (*#*************************************)
169 inline procedural "cic:/Coq/Reals/Rpower/limit1_ext.con" as theorem.
171 inline procedural "cic:/Coq/Reals/Rpower/limit1_imp.con" as theorem.
173 inline procedural "cic:/Coq/Reals/Rpower/Rinv_Rdiv.con" as theorem.
175 inline procedural "cic:/Coq/Reals/Rpower/Dln.con" as theorem.
177 inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_ln.con" as lemma.
179 inline procedural "cic:/Coq/Reals/Rpower/D_in_imp.con" as theorem.
181 inline procedural "cic:/Coq/Reals/Rpower/D_in_ext.con" as theorem.
183 inline procedural "cic:/Coq/Reals/Rpower/Dpower.con" as theorem.
185 inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_power.con" as theorem.