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<a NAME="E1:111"/><i><font color="Green" title="E93">A1</font></i>: 
<span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 16</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 16</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">255 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">673 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 97</span>)</span>
 
;<br/>
<a NAME="E2:111"/>
3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 64</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span> = 
3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default">32 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 32</span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E2:111_1"/>
3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 64</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 32</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then </b><span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 64</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 16</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 16</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="pepin.html#E115"><i><font color="Green" title="E91">Lm49</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
673 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 97
<b>by </b><i><a class="txt" href="pepin.html#E1:111"><i><font color="Green" title="E93">A1</font></i></a>, <a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E4:111"/>
<span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 64</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 673 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 97
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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