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

<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="algstr_3.html#NM2" title="ALGSTR_3:NM.2">Ternary-Field</a>; <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">a</font>, <font color="Olive" title="b2">a'</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">u'</font>, <font color="Olive" title="b6">v'</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a'</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">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="Olive" title="b5">u'</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b6">v'</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b2">a'</font>,<font color="Olive" title="b4">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="Olive" title="b5">u'</font>,<font color="Olive" title="b2">a'</font>,<font color="Olive" title="b6">v'</font> holds <br/>( <font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">u'</font> &amp; <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">v'</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a'</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">u'</font>, <font color="Maroon" title="c7">v'</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a'</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="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="c6">u'</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">v'</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="c3">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="c6">u'</font>,<font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c7">v'</font> implies ( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u'</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v'</font> ) )</span><br/>













<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a'</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E14">A2</font></i>: 
 <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="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="c6">u'</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">v'</font>
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green" title="E15">A3</font></i>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c3">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="c6">u'</font>,<font color="Maroon" title="c3">a'</font>,<font color="Maroon" title="c7">v'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u'</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v'</font> )</span><br/>

<a NAME="E4:22"/>
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u'</font>
 
<b>by </b><i><a class="txt" href="#E1:22"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E2:22"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E3:22"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u'</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v'</font> )
 <b>by </b><i><a class="txt" href="#E2:22"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</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>
