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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>thus </b><a NAME="E1:66"/>
2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> 
 ;<br/>

<b>assume </b><a NAME="E2:66"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E4:66"/><i><font color="Green" title="E49">A1</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">p</font>
 ;<br/>
<b>thus </b><a NAME="E5:66"/>
contradiction
 <b>by </b><i><a class="txt" href="fib_num2.html#E4:66"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>


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