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<b>let </b><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">u'</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v'</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u'</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">x</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">u'</font></span>)</span>;<br/>
<a NAME="E2:10"/>
<font color="Maroon" title="c1">u</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">u'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="algstr_3.html#E1:10"><i><font color="Green" title="E3">A1</font></i></a></i>;<br/>
<a NAME="E3:10"/><b>then </b><i><font color="Green" title="E4">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">u'</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">u'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c2">u'</font></span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E5:10"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="txt" href="algstr_3.html#E3:10"><i><font color="Green" title="E4">A2</font></i></a></i>;<br/>
<a NAME="E6:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">u'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v'</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c3">v</font>
 
;<br/>
<a NAME="E7:10"/><b>then </b><i><font color="Green" title="E5">A3</font></i>: 
<font color="Maroon" title="c1">u</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">u'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">v'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">v</font></span>)</span>
 
;<br/>
<b>take </b>
<font color="Maroon" title="c6">x</font>
;<br/>

<b>thus </b><a NAME="E8:10"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c4">v'</font>
 <b>by </b><i><a class="txt" href="algstr_3.html#E7:10"><i><font color="Green" title="E5">A3</font></i></a></i>;<br/>


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