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author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Tue, 17 Jan 2017 17:18:05 +0900
parents d4e4ecc1c347
children
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1 <!DOCTYPE html>
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2 <html>
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3 <head>
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4 <meta http-equiv="content-type" content="text/html;charset=utf-8">
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5 <title>証明によるプログラムの信頼性の向上(仮)</title>
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6
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7 <meta name="generator" content="Slide Show (S9) v2.5.0 on Ruby 2.3.0 (2015-12-25) [x86_64-darwin14]">
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8 <meta name="author" content="Yasutaka Higa" >
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9
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10 <!-- style sheet links -->
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11 <link rel="stylesheet" href="s6/themes/projection.css" media="screen,projection">
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12 <link rel="stylesheet" href="s6/themes/screen.css" media="screen">
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13 <link rel="stylesheet" href="s6/themes/print.css" media="print">
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14 <link rel="stylesheet" href="s6/themes/blank.css" media="screen,projection">
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16 <!-- JS -->
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17 <script src="s6/js/jquery-1.11.3.min.js"></script>
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18 <script src="s6/js/jquery.slideshow.js"></script>
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19 <script src="s6/js/jquery.slideshow.counter.js"></script>
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20 <script src="s6/js/jquery.slideshow.controls.js"></script>
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21 <script src="s6/js/jquery.slideshow.footer.js"></script>
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22 <script src="s6/js/jquery.slideshow.autoplay.js"></script>
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23
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24 <!-- prettify -->
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25 <link rel="stylesheet" href="scripts/prettify.css">
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26 <script src="scripts/prettify.js"></script>
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28 <script>
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29 $(document).ready( function() {
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30 Slideshow.init();
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32 $('code').each(function(_, el) {
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33 if (!el.classList.contains('noprettyprint')) {
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34 el.classList.add('prettyprint');
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35 el.style.display = 'block';
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36 }
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37 });
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38 prettyPrint();
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39 } );
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42 </script>
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43
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44 <!-- Better Browser Banner for Microsoft Internet Explorer (IE) -->
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45 <!--[if IE]>
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46 <script src="s6/js/jquery.microsoft.js"></script>
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47 <![endif]-->
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51 </head>
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52 <body>
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53
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54 <div class="layout">
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55 <div id="header"></div>
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56 <div id="footer">
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57 <div align="right">
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58 <img src="s6/images/logo.svg" width="200px">
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59 </div>
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60 </div>
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61 </div>
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63 <div class="presentation">
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65 <div class='slide cover'>
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66 <table width="90%" height="90%" border="0" align="center">
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67 <tr>
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68 <td>
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69 <div align="center">
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70 <h1><font color="#808db5">証明によるプログラムの信頼性の向上(仮)</font></h1>
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71 </div>
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72 </td>
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73 </tr>
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74 <tr>
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75 <td>
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76 <div align="left">
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77 Yasutaka Higa
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78 - profile not found -
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79 <hr style="color:#ffcc00;background-color:#ffcc00;text-align:left;border:none;width:100%;height:0.2em;">
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80 </div>
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81 </td>
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82 </tr>
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83 </table>
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84 </div>
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86 <div class='slide '>
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87 <!-- === begin markdown block ===
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89 generated by markdown/1.2.0 on Ruby 2.3.0 (2015-12-25) [x86_64-darwin14]
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90 on 2016-03-29 18:58:01 +0900 with Markdown engine kramdown (1.9.0)
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91 using options {}
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92 -->
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94 <!-- _S9SLIDE_ -->
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95 <h1 id="section">研究目的(仮)</h1>
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96
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97 <ul>
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98 <li>証明によるプログラムの信頼性の向上を目指す。</li>
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99 <li>信頼性とは、プログラムがプログラマの予期しない動作をしないことである。</li>
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100 <li>目標の例としては、現在は実行時にしか検出できないエラーなどを実行以前に検出することがある。</li>
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101 </ul>
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103
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104 </div>
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105 <div class='slide '>
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106 <!-- _S9SLIDE_ -->
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107 <h1 id="section-1">近況報告</h1>
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109 <ul>
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110 <li>ちょっとゲーデルの完全性定理と不完全性定理について調べた</li>
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111 <li>型システム入門 (Types and Programming Languages) を読み始めました</li>
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112 </ul>
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115 </div>
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116 <div class='slide '>
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117 <!-- _S9SLIDE_ -->
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118 <h1 id="section-2">ゲーデルの完全性定理</h1>
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120 <ul>
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121 <li>述語論理の完全性定理</li>
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122 <li>述語論理の論理式が真であれば、公理系の証明が存在する
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123 <ul>
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124 <li>これは完全性定理として証明されたらしい</li>
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125 </ul>
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126 </li>
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127 <li>一回述語論理のみらしい</li>
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128 <li>一回述語論理とは命題論理に量化記号を導入したもの
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129 <ul>
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130 <li>命題 : 人間は寝る</li>
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131 <li>量化された命題 : すべての人間は寝る</li>
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132 </ul>
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133 </li>
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134 </ul>
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135
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136
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137 </div>
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138 <div class='slide '>
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139 <!-- _S9SLIDE_ -->
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140 <h1 id="section-3">ゲーデルの不完全性定理</h1>
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141
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142 <ul>
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143 <li>自然数論の不完全性定理</li>
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144 <li>すべての命題は証明可能/反証可能、というわけではないらしい</li>
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145 <li>ゲーデル命題という「真であるにも関わらず、システムで証明可能で無い」命題が存在する</li>
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146 </ul>
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147
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148
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149 </div>
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150 <div class='slide '>
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151 <!-- _S9SLIDE_ -->
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152 <h1 id="section-4">ゲーデル命題の例</h1>
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153 <ul>
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154 <li>前提 : 真==証明可能、偽==反証可能 だとすると</li>
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155 <li>前提 : 証明可能な命題が真で、証明不可能な命題が偽であることが決定的</li>
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156 <li>例 : 「この命題はシステムによって証明可能では無い」
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157 <ul>
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158 <li>真なので反証はできない</li>
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159 <li>真なので証明可能かもしれないが、「証明可能で無い」という述語がついている</li>
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160 <li>よってシステムで決定不可能 == システムで証明できない</li>
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161 </ul>
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162 </li>
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163 </ul>
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164
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165
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166 </div>
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167 <div class='slide '>
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168 <!-- _S9SLIDE_ -->
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169 <h1 id="section-5">完全性定理と不完全性定理</h1>
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170
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171 <ul>
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172 <li>結局 : 具体的に何を意味するのかはあまり良く分かっていない</li>
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173 <li>論理は完全っぽくて自然数論は不完全っぽい、くらいの認識
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174 <ul>
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175 <li>論理は真であれば証明が存在する</li>
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176 <li>自然数論では証明が存在しないものがある</li>
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177 <li>なら論理と自然数論の違い……?</li>
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178 </ul>
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179 </li>
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180 <li>とりあえず、自己言及はしない方が良い、とかくらいの認識</li>
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181 </ul>
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182
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183
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184 </div>
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185 <div class='slide '>
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186 <!-- _S9SLIDE_ -->
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187 <h1 id="tapl">TaPL</h1>
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188 <ul>
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189 <li>型システム入門 - プログラミング言語と型の理論 -</li>
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190 <li>Types and Programming Languages</li>
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191 <li>まだ読み始めたばかりです</li>
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192 <li>型を使わない演算についてまでしか読んでません
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193 <ul>
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194 <li>bool と Church 数のみのラムダ演算</li>
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195 </ul>
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196 </li>
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197 </ul>
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198 <!-- === end markdown block === -->
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199 </div>
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200
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201
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202 </div><!-- presentation -->
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203 </body>
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204 </html>