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_calc.v,v 1.15.2.1 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.ma".
43 include "Reals/R_sqrt.ma".
46 Open Local Scope R_scope.
49 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI.con" as lemma.
51 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_3PI2.con" as lemma.
53 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_2PI.con" as lemma.
55 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_cos_PI4.con" as lemma.
57 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI3_cos_PI6.con" as lemma.
59 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI6_cos_PI3.con" as lemma.
61 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI6_RGT_0.con" as lemma.
63 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI6_RLT_PI2.con" as lemma.
65 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI6.con" as lemma.
67 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sqrt2_neq_0.con" as lemma.
69 inline procedural "cic:/Coq/Reals/Rtrigo_calc/R1_sqrt2_neq_0.con" as lemma.
71 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sqrt3_2_neq_0.con" as lemma.
73 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_sqrt2_0.con" as lemma.
75 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_sqrt3_0.con" as lemma.
77 inline procedural "cic:/Coq/Reals/Rtrigo_calc/PI4_RGT_0.con" as lemma.
79 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI4.con" as lemma.
81 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI4.con" as lemma.
83 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI4.con" as lemma.
85 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos3PI4.con" as lemma.
87 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin3PI4.con" as lemma.
89 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI6.con" as lemma.
91 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI6.con" as lemma.
93 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_PI3.con" as lemma.
95 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_PI3.con" as lemma.
97 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_PI3.con" as lemma.
99 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_2PI3.con" as lemma.
101 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_2PI3.con" as lemma.
103 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tan_2PI3.con" as lemma.
105 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cos_5PI4.con" as lemma.
107 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_5PI4.con" as lemma.
109 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_cos5PI4.con" as lemma.
111 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rgt_3PI2_0.con" as lemma.
113 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rgt_2PI_0.con" as lemma.
115 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_PI_3PI2.con" as lemma.
117 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rlt_3PI2_2PI.con" as lemma.
119 (*#**************************************************************)
121 (* Radian -> Degree | Degree -> Radian *)
123 (*#**************************************************************)
125 inline procedural "cic:/Coq/Reals/Rtrigo_calc/plat.con" as definition.
127 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toRad.con" as definition.
129 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toDeg.con" as definition.
131 inline procedural "cic:/Coq/Reals/Rtrigo_calc/rad_deg.con" as lemma.
133 inline procedural "cic:/Coq/Reals/Rtrigo_calc/toRad_inj.con" as lemma.
135 inline procedural "cic:/Coq/Reals/Rtrigo_calc/deg_rad.con" as lemma.
137 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sind.con" as definition.
139 inline procedural "cic:/Coq/Reals/Rtrigo_calc/cosd.con" as definition.
141 inline procedural "cic:/Coq/Reals/Rtrigo_calc/tand.con" as definition.
143 inline procedural "cic:/Coq/Reals/Rtrigo_calc/Rsqr_sin_cos_d_one.con" as lemma.
145 (*#**************************************************)
147 (* Other properties *)
149 (*#**************************************************)
151 inline procedural "cic:/Coq/Reals/Rtrigo_calc/sin_lb_ge_0.con" as lemma.