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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">a'</font>, <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">u'</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">v'</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K4" title="ALGSTR_3:func.4">TernaryFieldEx</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u'</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">v'</font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u'</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c6">v'</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">aa</font> = <font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c8">aa'</font> = <font color="Maroon" title="c2">a'</font>, <font color="Maroon" title="c9">uu</font> = <font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c10">uu'</font> = <font color="Maroon" title="c4">u'</font>, <font color="Maroon" title="c11">vv</font> = <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c12">vv'</font> = <font color="Maroon" title="c6">v'</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E4:19"/>
(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c11">vv</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u'</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c6">v'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c12">vv'</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c11">vv</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u'</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c6">v'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c12">vv'</font> )
 
<b>by </b><i><a class="ref" href="algstr_3.html#T5" target="_self" title="ALGSTR_3:th.5">Th5</a></i>;<br/>
<a NAME="E5:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">vv</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c11">vv</font></span>)</span></span>)</span> <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="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c12">vv'</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c12">vv'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="algstr_3.html#E1:19"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="algstr_3.html#E2:19"><i><font color="Green" title="E15">A2</font></i></a></i>;<br/>
<a NAME="E6:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</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="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</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="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:19"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</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="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">aa</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="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">aa'</font></span>)</span>
 
;<br/>
<a NAME="E8:19"/><b>then </b>
<font color="Maroon" title="c9">uu</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">aa</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">aa'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">uu'</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">aa</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">aa'</font></span>)</span>
 
;<br/>
<a NAME="E9:19"/><b>then </b>
( <font color="Maroon" title="c9">uu</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">uu'</font> or <font color="Maroon" title="c7">aa</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">aa'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T5" title="XCMPLX_1:th.5">XCMPLX_1:5</a></i>;<br/>
<b>hence </b><a NAME="E10:19"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a'</font> or <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u'</font> )
 ;<br/>


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