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<div class="add">

<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>

<a NAME="E1:7"/>
( 0 <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> implies <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1"/>
0 <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">a1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:7_1"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">a1</font>
 <b>by </b><i><a class="ref" href="int_1.html#D9" title="INT_1:def.9">INT_1:def 9</a></i>;<br/>
<b>thus </b><a NAME="E4:7_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="int_2.html#E3:7_1"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:7"/>
( 0 <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> iff <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 ;<br/>


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