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<b>let </b><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">l</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<div><i><font color="Green" title="E26">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1"/>
<font color="Maroon" title="c1">k</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">l</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c3">m</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:26_1"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">m</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="E4:26_1"/>
<font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">k</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:26"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="wsierp_1.html#E3:26_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_2"/>
<font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">k</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c3">m</font> = <font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">k</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><a NAME="E3:26_2"/>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:26"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><b>hence </b><a NAME="E4:26_2"/>
<font color="Maroon" title="c1">k</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">l</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/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26"/>
( <font color="Maroon" title="c1">k</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">l</font> iff <font color="Maroon" title="c2">l</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c1">k</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:26"><i><font color="Green" title="E26">A2</font></i></a></i>;<br/>


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