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<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>consider </b><font color="Maroon" title="c2">m</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>, <font color="Maroon" title="c3">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E2:12"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c3">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> 
 <b>and </b><br/><a NAME="E3:12"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="rat_1.html#T24" title="RAT_1:th.24">RAT_1:24</a></i>;<br/>
<b>assume </b><a NAME="E4:12"/>
<font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E5:12"/><b>then </b>
( ( <font color="Maroon" title="c3">k</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>  &amp; <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) or ( <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 
<b>by </b><i><a class="txt" href="real_3.html#E2:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="real_3.html#E3:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="real_2.html#T134" title="REAL_2:th.134">REAL_2:134</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">m</font> = <font color="Maroon" title="c2">m</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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">m</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c3">k</font>
;<br/>

<b>thus </b><a NAME="E7:12"/>
( <font color="Maroon" title="c3">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>  &amp; <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="txt" href="real_3.html#E2:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="real_3.html#E3:12"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/>


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