<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">u'</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">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u'</font> implies for <font color="Olive" title="b1">v</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>   ex <font color="Olive" title="b3">a</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  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">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="c2">u'</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">v'</font> )</span><br/>

<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E11">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>
 ; <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">v</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>   ex <font color="Olive" title="b3">a</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  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">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="c2">u'</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">v'</font></span><br/>

<b>let </b><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v'</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">a</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  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">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="c2">u'</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">v'</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c5">uu</font> = <font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c6">uu'</font> = <font color="Maroon" title="c2">u'</font>, <font color="Maroon" title="c7">vv</font> = <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c8">vv'</font> = <font color="Maroon" title="c4">v'</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>consider </b><font color="Maroon" title="c9">aa</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:17"/><i><font color="Green" title="E12">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">uu</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">vv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">uu'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">vv'</font>
 <b>by </b><i><a class="txt" href="algstr_3.html#E1:17"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="algstr_3.html#T3" target="_self" title="ALGSTR_3:th.3">Th3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c9">aa</font> 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/>
<a NAME="E6:17"/>
(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c10">a</font>,<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="c5">uu</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">vv</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c2">u'</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c4">v'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">uu'</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">vv'</font> )
 
<b>by </b><i><a class="ref" href="algstr_3.html#D4" target="_self" title="ALGSTR_3:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E7:17"/>
 ex <font color="Olive" title="b1">a</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  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">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="c2">u'</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">v'</font>
 <b>by </b><i><a class="txt" href="algstr_3.html#E4:17"><i><font color="Green" title="E12">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
