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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">a'</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a'</font> implies for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">b'</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>   ex <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>  st <br/>(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b'</font> ) )</span><br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">b'</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>   ex <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>  st <br/>(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b'</font> )</span><br/>

<b>let </b><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">b'</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>  st <br/>(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b1">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b1">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b'</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c2">a'</font>, <font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c8">y'</font> = <font color="Maroon" title="c4">b'</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>set </b><font color="Maroon" title="c9">s</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">t</font> = <font color="Maroon" title="c7">y</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">u</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span>, <font color="Maroon" title="c12">v</font> = <font color="Maroon" title="c7">y</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span> as   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c11">u</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">v</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a>  st <br/>(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b'</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c12">v</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c12">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c12">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b'</font> )</span><br/>

<b>thus </b> <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c12">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">y</font></span>)</span>
<b>by </b><i><a class="ref" href="algstr_3.html#D4" target="_self" title="ALGSTR_3:def.4">Def4</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c12">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b'</font></span><br/>

<a NAME="E5:16"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="#E1:16"><i><font color="Green" title="E10">A1</font></i></a></i>;<br/>
<b>thus </b> <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c2">a'</font>,<font color="Maroon" title="c12">v</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x'</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">y</font></span>)</span>
<b>by </b><i><a class="ref" href="algstr_3.html#D4" target="_self" title="ALGSTR_3:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">y</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">y'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">y</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">y</font>
<b>by </b><i><a class="txt" href="#E5:16"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>
<br/>.= 
<font color="Maroon" title="c4">b'</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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