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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green">E31</font></i>: 
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:10"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>
<a NAME="E4:10"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>thus </b><font color="Maroon">n</font> <a href="power.html#K2" target="_self">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="prepower.html#K5">-Root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i>, <a class="ref" href="prepower.html#T29">PREPOWER:29</a></i>
;<br/>


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