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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="E1:54"/><i><font color="Green">E41</font></i>: 
1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E2:54"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> 0 <a href="nat_1.html#R1">divides</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:54_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="nat_1.html#R1">divides</a> 1
 ;<br/><a NAME="E2:54_1"/><b>then </b>
<font color="Maroon">n</font> <a href="newton.html#K2">|^</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T54">NAT_1:54</a></i>;<br/><a NAME="E3:54_1"/><b>then </b>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/><a NAME="E4:54_1"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="cqc_the1.html#T2">CQC_THE1:2</a></i>;<br/><a NAME="E5:54_1"/><b>then </b>
0 <a href="nat_1.html#R1">divides</a> 1
 <b>by </b><i>, <a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/><b>hence </b><a NAME="E6:54_1"/>
contradiction
 <b>by </b><i><a class="ref" href="int_2.html#T3">INT_2:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:54"/>
<font color="Maroon">n</font> <a href="nat_3.html#K11" target="_self">|-count</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , </i>;<br/>


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