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19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
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33 (*i $Id: Rsqrt_def.v,v 1.14.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)
35 include "Bool/Sumbool.ma".
37 include "Reals/Rbase.ma".
39 include "Reals/Rfunctions.ma".
41 include "Reals/SeqSeries.ma".
43 include "Reals/Ranalysis1.ma".
46 Open Local Scope R_scope.
49 inline procedural "cic:/Coq/Reals/Rsqrt_def/Dichotomy_lb.con" as definition.
51 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb.con" as definition.
53 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up.con" as definition.
57 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_comp.con" as lemma.
59 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_growing.con" as lemma.
61 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_decreasing.con" as lemma.
63 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_maj_y.con" as lemma.
65 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_maj.con" as lemma.
67 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_min_x.con" as lemma.
69 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_min.con" as lemma.
71 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_cv.con" as lemma.
73 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_cv.con" as lemma.
75 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_dicho_up.con" as lemma.
77 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n.con" as definition.
79 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_neq_R0.con" as lemma.
81 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_growing.con" as lemma.
83 inline procedural "cic:/Coq/Reals/Rsqrt_def/pow_2_n_infty.con" as lemma.
85 inline procedural "cic:/Coq/Reals/Rsqrt_def/cv_dicho.con" as lemma.
87 inline procedural "cic:/Coq/Reals/Rsqrt_def/cond_positivity.con" as definition.
89 (* Sequential caracterisation of continuity *)
91 inline procedural "cic:/Coq/Reals/Rsqrt_def/continuity_seq.con" as lemma.
93 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_lb_car.con" as lemma.
95 inline procedural "cic:/Coq/Reals/Rsqrt_def/dicho_up_car.con" as lemma.
97 (* Intermediate Value Theorem *)
99 inline procedural "cic:/Coq/Reals/Rsqrt_def/IVT.con" as lemma.
101 inline procedural "cic:/Coq/Reals/Rsqrt_def/IVT_cor.con" as lemma.
103 (* We can now define the square root function as the reciprocal transformation of the square root function *)
105 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_exists.con" as lemma.
107 (* Definition of the square root: R+->R *)
109 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt.con" as definition.
113 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_positivity.con" as lemma.
117 inline procedural "cic:/Coq/Reals/Rsqrt_def/Rsqrt_Rsqrt.con" as lemma.