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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:4_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="abian.html#V1" target="_self">even</a>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:4_1_1_1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="abian.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E4:4_1_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E5:4_1_1_1"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="abian.html#E3:4_1_1_1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="square_1.html#T25">SQUARE_1:25</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><b>take </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font>;<br/><b>thus </b><a NAME="E7:4_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="abian.html#E3:4_1_1_1"><i><font color="Green">E2</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:4_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E3:4_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="abian.html#V1" target="_self">even</a>
 <b>by </b><i><a class="ref" href="abian.html#D1" target="_self">Def1</a></i>;<br/>


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