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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:3_1_1_1"/>
<font color="Maroon" title="c1">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c2">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:3_1_1_1"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">k</font>
 <b>by </b><i><a class="ref" href="abian.html#D1" target="_self" title="ABIAN:def.1">Def1</a></i>;<br/><a NAME="E4:3_1_1_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/><a NAME="E5:3_1_1_1"/><b>then </b>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">k</font>
 <b>by </b><i><a class="txt" href="abian.html#E3:3_1_1_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="square_1.html#T25" title="SQUARE_1:th.25">SQUARE_1:25</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c3">k</font> = <font color="Maroon" title="c2">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><b>take </b><font color="Maroon" title="c4">k</font> = <font color="Maroon" title="c3">k</font>;<br/><b>thus </b><a NAME="E7:3_1_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="txt" href="abian.html#E3:3_1_1_1"><i><font color="Green" title="E2">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:3_1_1"/>
 ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">k</font>
 ;<br/>

<b>hence </b><a NAME="E3:3_1_1"/>
<font color="Maroon" title="c1">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 <b>by </b><i><a class="ref" href="abian.html#D1" target="_self" title="ABIAN:def.1">Def1</a></i>;<br/>


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