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<b>let </b><font color="Maroon">a</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> , <font color="Maroon">a'</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> , <font color="Maroon">u</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> , <font color="Maroon">u'</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> , <font color="Maroon">v</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> , <font color="Maroon">v'</font> be   <a href="algstr_3.html#NM1">Scalar</a> of <a href="algstr_3.html#K4" target="_self">TernaryFieldEx</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E24</font></i>: 
 <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u</font>,<font color="Maroon">a</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u'</font>,<font color="Maroon">a</font>,<font color="Maroon">v'</font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E25</font></i>: 
 <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u</font>,<font color="Maroon">a'</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u'</font>,<font color="Maroon">a'</font>,<font color="Maroon">v'</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">aa</font> = <font color="Maroon">a</font>, <font color="Maroon">aa'</font> = <font color="Maroon">a'</font>, <font color="Maroon">uu</font> = <font color="Maroon">u</font>, <font color="Maroon">uu'</font> = <font color="Maroon">u'</font>, <font color="Maroon">vv</font> = <font color="Maroon">v</font>, <font color="Maroon">vv'</font> = <font color="Maroon">v'</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E4:19"/>
(  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u</font>,<font color="Maroon">a</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv</font> &amp;  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u'</font>,<font color="Maroon">a</font>,<font color="Maroon">v'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv'</font> &amp;  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u</font>,<font color="Maroon">a'</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv</font> &amp;  <a href="algstr_3.html#K1" target="_self">Tern</a> <font color="Maroon">u'</font>,<font color="Maroon">a'</font>,<font color="Maroon">v'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv'</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">vv</font> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv'</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">vv'</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">aa'</font></span>)</span>
 
;<br/>
<a NAME="E8:19"/><b>then </b>
<font color="Maroon">uu</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">aa</font> <a href="real_1.html#K5">-</a> <font color="Maroon">aa'</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">uu'</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">aa</font> <a href="real_1.html#K5">-</a> <font color="Maroon">aa'</font></span>)</span>
 
;<br/>
<a NAME="E9:19"/><b>then </b>
( <font color="Maroon">uu</font> <a href="hidden.html#R1">=</a> <font color="Maroon">uu'</font> or <font color="Maroon">aa</font> <a href="real_1.html#K5">-</a> <font color="Maroon">aa'</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/>
<b>hence </b><a NAME="E10:19"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> or <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u'</font> )
 ;<br/>


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