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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:230"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>then consider </b><font color="Maroon">c</font> being  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:230"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T234">XCMPLX_1:234</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="230_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:230_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="230_1_1"><b>suppose </b></a><a NAME="E1:230_1_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:230_1_1"/>
 ex <font color="Olive">c</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Olive">c</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="230_1_2"><b>suppose </b></a><a NAME="E1:230_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:230_1_2"/><b>then </b>
<font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T50">XCMPLX_1:50</a></i>;<br/><a NAME="E3:230_1_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T54">XCMPLX_1:54</a></i>;<br/><b>then reconsider </b><font color="Maroon">c</font> = <font color="Maroon">c</font> as  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  ;<br/><b>take </b>
<font color="Maroon">c</font>
;<br/><b>thus </b><a NAME="E5:230_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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