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auto-Update generated slides by script
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 02 Sep 2014 18:03:20 +0900
parents dfd2f6a3c82d
children d4e4ecc1c347
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1 <!DOCTYPE HTML>
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2
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3 <html lang="Japanese">
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4 <head>
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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 <meta charset="UTF-8">
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7 <meta name="viewport" content="width=1274, user-scalable=no">
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8 <meta name="generator" content="Slide Show (S9)">
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9 <meta name="author" content="Yasutaka Higa">
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10 <link rel="stylesheet" href="themes/ribbon/styles/style.css">
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11 <style>
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12 #Cover H2 {
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13 color:#FFF;
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14 text-align:center;
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15 font-size:70px;
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16 }
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17 </style>
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18 </head>
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19 <body class="list">
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20 <header class="caption">
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21 <h1>証明によるプログラムの信頼性の向上(仮)</h1>
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22 <p>Yasutaka Higa</p>
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23 </header>
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24 <div class="slide bg" id="Cover"><div>
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25 <section>
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26 <header>
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27 <h2>証明によるプログラムの信頼性の向上(仮)</h2>
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28 </header>
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29
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30 <img src="pictures/" alt="">
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31 <!-- © John Carey, http://fiftyfootshadows.net/ -->
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32 </section>
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33 </div></div>
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34
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35 <!-- todo: add slide.classes to div -->
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36 <!-- todo: create slide id from header? like a slug in blogs? -->
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37
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38 <div class="slide" id="2"><div>
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39 <section>
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40 <header>
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41 <h1 id="section">研究目的(仮)</h1>
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42 </header>
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43 <!-- === begin markdown block ===
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44
34
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45 generated by markdown 1.1.1 on Ruby 2.1.2 (2014-05-08) [x86_64-darwin13.0]
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46 on 2014-08-05 16:09:14 +0900 with Markdown engine kramdown (1.3.3)
4
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47 using options {}
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48 -->
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49
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50 <!-- _S9SLIDE_ -->
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51
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52
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53 <ul>
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54 <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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55 <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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56 <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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57 </ul>
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60
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61 </section>
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62 </div></div>
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63
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64 <div class="slide" id="3"><div>
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65 <section>
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66 <header>
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67 <h1 id="section-1">近況報告</h1>
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68 </header>
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69 <!-- _S9SLIDE_ -->
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71
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72 <ul>
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73 <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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74 <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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75 </ul>
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76
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78
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79 </section>
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80 </div></div>
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81
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82 <div class="slide" id="4"><div>
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83 <section>
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84 <header>
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85 <h1 id="section-2">ゲーデルの完全性定理</h1>
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86 </header>
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87 <!-- _S9SLIDE_ -->
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88
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89
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90 <ul>
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91 <li>述語論理の完全性定理</li>
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92 <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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93 <ul>
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94 <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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95 </ul>
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96 </li>
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97 <li>一回述語論理のみらしい</li>
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98 <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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99 <ul>
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100 <li>命題 : 人間は寝る</li>
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101 <li>量化された命題 : すべての人間は寝る</li>
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102 </ul>
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103 </li>
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104 </ul>
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107
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108 </section>
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109 </div></div>
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110
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111 <div class="slide" id="5"><div>
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112 <section>
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113 <header>
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114 <h1 id="section-3">ゲーデルの不完全性定理</h1>
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115 </header>
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116 <!-- _S9SLIDE_ -->
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117
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118
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119 <ul>
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120 <li>自然数論の不完全性定理</li>
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121 <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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122 <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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123 </ul>
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124
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125
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126
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127 </section>
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128 </div></div>
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130 <div class="slide" id="6"><div>
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131 <section>
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132 <header>
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133 <h1 id="section-4">ゲーデル命題の例</h1>
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134 </header>
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135 <!-- _S9SLIDE_ -->
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136
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137 <ul>
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138 <li>前提 : 真==証明可能、偽==反証可能 だとすると</li>
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139 <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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140 <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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141 <ul>
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142 <li>真なので反証はできない</li>
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143 <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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144 <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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145 </ul>
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146 </li>
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147 </ul>
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148
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149
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150
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151 </section>
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152 </div></div>
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153
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154 <div class="slide" id="7"><div>
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155 <section>
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156 <header>
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157 <h1 id="section-5">完全性定理と不完全性定理</h1>
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158 </header>
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159 <!-- _S9SLIDE_ -->
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160
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161
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162 <ul>
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163 <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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164 <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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165 <ul>
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166 <li>論理は真であれば証明が存在する</li>
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167 <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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168 <li>なら論理と自然数論の違い……？</li>
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169 </ul>
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170 </li>
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171 <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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172 </ul>
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173
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174
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175
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176 </section>
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177 </div></div>
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178
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179 <div class="slide" id="8"><div>
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180 <section>
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181 <header>
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182 <h1 id="tapl">TaPL</h1>
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183 </header>
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184 <!-- _S9SLIDE_ -->
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185
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186 <ul>
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187 <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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188 <li>Types and Programming Languages</li>
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189 <li>まだ読み始めたばかりです</li>
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190 <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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191 <ul>
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192 <li>bool と Church 数のみのラムダ演算</li>
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193 </ul>
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194 </li>
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195 </ul>
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196 <!-- === end markdown block === -->
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197
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198 </section>
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199 </div></div>
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200
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201
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202 <!--
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203 To hide progress bar from entire presentation
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204 just remove “progress” element.
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205 -->
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206 <div class="progress"><div></div></div>
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207 <script src="scripts/script.js"></script>
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208 <!-- Copyright © 2010–2011 Vadim Makeev, http://pepelsbey.net/ -->
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209 </body>
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210 </html>