helm/software/matita/contribs/procedural/Coq/Reals/R_sqrt.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: R_sqrt.v,v 1.10.2.1 2004/07/16 19:31:12 herbelin Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/Rsqrt_def.ma".
  40
  41 (* UNEXPORTED
  42 Open Local Scope R_scope.
  43 *)
  44
  45 (* Here is a continuous extension of Rsqrt on R *)
  46
  47 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt.con" as definition.
  48
  49 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_positivity.con" as lemma.
  50
  51 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_sqrt.con" as lemma.
  52
  53 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_0.con" as lemma.
  54
  55 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_1.con" as lemma.
  56
  57 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_eq_0.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lem_0.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Reals/R_sqrt/sqtr_lem_1.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_def.con" as lemma.
  64
  65 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_square.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_Rsqr.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_Rsqr_abs.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sqrt.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_mult.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_R0.con" as lemma.
  76
  77 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_div.con" as lemma.
  78
  79 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_0.con" as lemma.
  80
  81 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_lt_1.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_le_0.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_le_1.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_inj.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_less.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_more.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Reals/R_sqrt/sqrt_cauchy.con" as lemma.
  94
  95 (*#***********************************************************)
  96
  97 (* Resolution of [a*X^2+b*X+c=0]                            *)
  98
  99 (*#***********************************************************)
 100
 101 inline procedural "cic:/Coq/Reals/R_sqrt/Delta.con" as definition.
 102
 103 inline procedural "cic:/Coq/Reals/R_sqrt/Delta_is_pos.con" as definition.
 104
 105 inline procedural "cic:/Coq/Reals/R_sqrt/sol_x1.con" as definition.
 106
 107 inline procedural "cic:/Coq/Reals/R_sqrt/sol_x2.con" as definition.
 108
 109 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sol_eq_0_1.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Reals/R_sqrt/Rsqr_sol_eq_0_0.con" as lemma.
 112