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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">q</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E35</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">q</font> <a href="prepower.html#K3">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E3:1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E4:1"/>
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , <a class="ref" href="prepower.html#T21">PREPOWER:21</a></i>;<br/>
<a NAME="E5:1"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E6:1"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/>
<a NAME="E7:1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E8:1"/><b>then </b>
<font color="Maroon">q</font> <a href="prepower.html#K7">#Z</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 
<b>by </b><i><a class="ref" href="prepower.html#T45">PREPOWER:45</a></i>;<br/>
<b>hence </b><a NAME="E9:1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="prepower.html#T46">PREPOWER:46</a></i>;<br/>


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