helm/software/matita/contribs/procedural/Coq/Reals/Sqrt_reg.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___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
  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: Sqrt_reg.v,v 1.9 2003/12/24 10:27:08 barras Exp $ i*)
  34
  35 include "Reals/Rbase.ma".
  36
  37 include "Reals/Rfunctions.ma".
  38
  39 include "Reals/Ranalysis1.ma".
  40
  41 include "Reals/R_sqrt.ma".
  42
  43 (* UNEXPORTED
  44 Open Local Scope R_scope.
  45 *)
  46
  47 (*#*********)
  48
  49 inline procedural "cic:/Coq/Reals/Sqrt_reg/sqrt_var_maj.con" as lemma.
  50
  51 (* sqrt is continuous in 1 *)
  52
  53 inline procedural "cic:/Coq/Reals/Sqrt_reg/sqrt_continuity_pt_R1.con" as lemma.
  54
  55 (* sqrt is continuous forall x>0 *)
  56
  57 inline procedural "cic:/Coq/Reals/Sqrt_reg/sqrt_continuity_pt.con" as lemma.
  58
  59 (* sqrt is derivable for all x>0 *)
  60
  61 inline procedural "cic:/Coq/Reals/Sqrt_reg/derivable_pt_lim_sqrt.con" as lemma.
  62
  63 (*#*********)
  64
  65 inline procedural "cic:/Coq/Reals/Sqrt_reg/derivable_pt_sqrt.con" as lemma.
  66
  67 (*#*********)
  68
  69 inline procedural "cic:/Coq/Reals/Sqrt_reg/derive_pt_sqrt.con" as lemma.
  70
  71 (* We show that sqrt is continuous for all x>=0 *)
  72
  73 (* Remark : by definition of sqrt (as extension of Rsqrt on |R), *)
  74
  75 (*          we could also show that sqrt is continuous for all x *)
  76
  77 inline procedural "cic:/Coq/Reals/Sqrt_reg/continuity_pt_sqrt.con" as lemma.
  78