<?xml version="1.0"?>
<div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 317 &amp; <font color="Maroon" title="c1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  implies  not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317 )</span><br/><a NAME="E1:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 158</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E2:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A1</font></span>: 
not 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E3:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 105</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 ;<br/><a NAME="E4:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A2</font></span>: 
not 3 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E5:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 24</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5
 ;<br/><a NAME="E6:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A3</font></span>: 
not 13 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E7:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">11 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 28</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9
 ;<br/><a NAME="E8:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A4</font></span>: 
not 11 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E9:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">19 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 16</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 13
 ;<br/><a NAME="E10:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A5</font></span>: 
not 19 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E11:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">17 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 18</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 11
 ;<br/><a NAME="E12:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A6</font></span>: 
not 17 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E13:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">23 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 13</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 18
 ;<br/><a NAME="E14:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A7</font></span>: 
not 23 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E15:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 45</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 ;<br/><a NAME="E16:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A8</font></span>: 
not 7 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><a NAME="E17:42_1"/>
317 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 63</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 ;<br/><a NAME="E18:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A9</font></span>: 
not 5 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T9" target="_self" title="NAT_4:th.9">Th9</a></span>;<br/><span class="kw">assume </span><a NAME="E19:42_1"/>
( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 317 &amp; <font color="Maroon" title="c1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317</span><br/><span class="kw">hence </span><a NAME="E20:42_1"/>
not <font color="Maroon" title="c1">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 317
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_1"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E4:42_1"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="txt" href="#E18:42_1"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="txt" href="#E16:42_1"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="txt" href="#E8:42_1"><span class="lab"><font color="Green" title="E43">A4</font></span></a>, <a class="txt" href="#E6:42_1"><span class="lab"><font color="Green" title="E42">A3</font></span></a>, <a class="txt" href="#E12:42_1"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="txt" href="#E10:42_1"><span class="lab"><font color="Green" title="E44">A5</font></span></a>, <a class="txt" href="#E14:42_1"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="txt" href="nat_4.html#E36"><span class="lab"><font color="Green" title="E33">Lm6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:42"/>
317 is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_4.html#T14" target="_self" title="NAT_4:th.14">Th14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
