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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">i1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c1">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">i1</font> &amp; <font color="Maroon" title="c2">i1</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/>

<a NAME="E2:12"/><b>then </b>
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c2">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="absvalue.html#T7" title="ABSVALUE:th.7">ABSVALUE:7</a></i>;<br/>
<a NAME="E3:12"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c2">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E4:12"/>
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c1">i</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c2">i1</font>
 
<b>by </b><i><a class="txt" href="int_4.html#E1:12"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="int_2.html#T21" title="INT_2:th.21">INT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E5:12"/>
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <font color="Maroon" title="c2">i1</font>
 <b>by </b><i><a class="txt" href="int_4.html#E3:12"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="nat_d.html#T7" title="NAT_D:th.7">NAT_D:7</a></i>;<br/>


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