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: Rtrigo_def.v,v 1.17.2.1 2004/07/16 19:31:14 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/SeqSeries.ma".
41 include "Reals/Rtrigo_fun.ma".
43 include "Arith/Max.ma".
46 Open Local Scope R_scope.
49 (*#****************************)
51 (* Definition of exponential *)
53 (*#****************************)
55 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_in.con" as definition.
57 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_cof_no_R0.con" as lemma.
59 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_exp.con" as lemma.
61 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp.con" as definition.
63 inline procedural "cic:/Coq/Reals/Rtrigo_def/pow_i.con" as lemma.
65 (*i Calculus of $e^0$ *)
67 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_exp0.con" as lemma.
69 inline procedural "cic:/Coq/Reals/Rtrigo_def/exp_0.con" as lemma.
71 (*#*************************************)
73 (* Definition of hyperbolic functions *)
75 (*#*************************************)
77 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosh.con" as definition.
79 inline procedural "cic:/Coq/Reals/Rtrigo_def/sinh.con" as definition.
81 inline procedural "cic:/Coq/Reals/Rtrigo_def/tanh.con" as definition.
83 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosh_0.con" as lemma.
85 inline procedural "cic:/Coq/Reals/Rtrigo_def/sinh_0.con" as lemma.
87 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_n.con" as definition.
89 inline procedural "cic:/Coq/Reals/Rtrigo_def/simpl_cos_n.con" as lemma.
91 inline procedural "cic:/Coq/Reals/Rtrigo_def/archimed_cor1.con" as lemma.
93 inline procedural "cic:/Coq/Reals/Rtrigo_def/Alembert_cos.con" as lemma.
95 inline procedural "cic:/Coq/Reals/Rtrigo_def/cosn_no_R0.con" as lemma.
99 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_in.con" as definition.
103 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_cos.con" as lemma.
105 (* Definition of cosinus *)
107 (*#************************)
109 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos.con" as definition.
111 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_n.con" as definition.
113 inline procedural "cic:/Coq/Reals/Rtrigo_def/simpl_sin_n.con" as lemma.
115 inline procedural "cic:/Coq/Reals/Rtrigo_def/Alembert_sin.con" as lemma.
117 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_no_R0.con" as lemma.
121 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_in.con" as definition.
125 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_sin.con" as lemma.
127 (*#**********************)
129 (* Definition of sinus *)
131 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin.con" as definition.
133 (*#********************************************)
137 (*#********************************************)
139 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_sym.con" as lemma.
141 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_antisym.con" as lemma.
143 inline procedural "cic:/Coq/Reals/Rtrigo_def/sin_0.con" as lemma.
145 inline procedural "cic:/Coq/Reals/Rtrigo_def/exist_cos0.con" as lemma.
147 (* Calculus of (cos 0) *)
149 inline procedural "cic:/Coq/Reals/Rtrigo_def/cos_0.con" as lemma.