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<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">r3</font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">r1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>thus </b><a NAME="E3:1"/>
( <font color="Maroon">r3</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font> implies <font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">r3</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font>
 ;<br/>

<font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r3</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>
;<br/>
<b>hence </b><a NAME="E3:1_1"/>
<font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font>
 ;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E4:1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font>
 ;<br/>

<font color="Maroon">r3</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> 1</span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font>
<b>by </b><i>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font>
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T4">XCMPLX_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> 1
<b>by </b><i>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font>

;<br/>
<b>hence </b><a NAME="E6:1"/>
<font color="Maroon">r3</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">r</font>
 ;<br/>


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