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

<b>assume </b><a NAME="E1:23"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">nn</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">nn'</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:23"/>
<font color="Maroon">nn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">nn'</font>
 ;<br/>

<a NAME="E3:23"/><b>then </b>
<font color="Maroon">nn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">nn'</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">nn'</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<b>hence </b><a NAME="E4:23"/>
contradiction
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>


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