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<b>let </b><font color="Maroon">n</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:55"/><i><font color="Green">E41</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E3:55"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> 1 <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_1"/>
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:55_1"/><b>then </b>
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T54">NAT_1:54</a></i>;<br/><b>hence </b><a NAME="E3:55_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="prepower.html#T21">PREPOWER:21</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:55"/>
<font color="Maroon">n</font> <a href="nat_3.html#K11" target="_self">|-count</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, , </i>;<br/>


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