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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E32</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 19 &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> )
 ;<br/><a NAME="E2:33_1"/>
19 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K24">*</a> 9</span>)</span> <a href="binop_2.html#K23">+</a> 1
 ;<br/><a NAME="E3:33_1"/><b>then </b><i><font color="Green">E33</font></i>: 
not 2 <a href="nat_1.html#R1">divides</a> 19
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self">Th9</a></i>;<br/><a NAME="E4:33_1"/>
19 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24">*</a> 6</span>)</span> <a href="binop_2.html#K23">+</a> 1
 ;<br/><a NAME="E5:33_1"/><b>then </b>
not 3 <a href="nat_1.html#R1">divides</a> 19
 <b>by </b><i><a class="ref" href="nat_4.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E6:33_1"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> 19
 <b>by </b><i><a class="txt" href="nat_4.html#E1:33_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="nat_4.html#E3:33_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="nat_4.html#E28"><i><font color="Green">Lemma28</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:33"/>
19 is <a href="int_2.html#V1">prime</a>
 <b>by </b><i><a class="ref" href="nat_4.html#T14" target="_self">Th14</a></i>;<br/>


</div>
