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

<b>let </b><font color="Maroon">AFV</font> be  <a href="analoaf.html#V1">strict</a> <a href="tdgroup.html#NM3">AffVect</a>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font>;<br/>



<b>set </b><font color="Maroon">X</font> =  <a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font>;<br/>
<a NAME="E1:72"/><i><font color="Green">E22</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="tdgroup.html#K2">AV</a> <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font>
 
<b>by </b><i><a class="ref" href="tdgroup.html#T9">TDGROUP:9</a></i>;<br/>
<a NAME="E2:72"/>
 <a href="tdgroup.html#K1">CONGRD</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">AFV</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>set </b><font color="Maroon">xy</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span>;<br/><div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:72_1_1_1"/><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="tdgroup.html#K1">CONGRD</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>
 ;<br/><b>set </b><font color="Maroon">V</font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>;<br/><b>set </b><font color="Maroon">VV</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><a NAME="E2:72_1_1_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:72_1_1_1"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="afvect0.html#T24" target="_self">Th24</a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><a NAME="E4:72_1_1_1"/><b>then </b><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T10">MCART_1:10</a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/><b>reconsider </b><font color="Maroon">x1'</font> = <font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">x2'</font> = <font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a> , <font color="Maroon">y1'</font> = <font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">y2'</font> = <font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a>  as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> <b>by </b><i><a class="ref" href="afvect0.html#T25" target="_self">Th25</a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x1'</font>, <font color="Maroon">x2</font> = <font color="Maroon">x2'</font>, <font color="Maroon">y1</font> = <font color="Maroon">y1'</font>, <font color="Maroon">y2</font> = <font color="Maroon">y2'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> ;<br/><b>set </b><font color="Maroon">z1'</font> = <font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font>;<br/><b>set </b><font color="Maroon">z2'</font> = <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font>;<br/><a NAME="E7:72_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font>
 <b>by </b><i><a class="ref" href="afvect0.html#T24" target="_self">Th24</a>, <a class="ref" href="afvect0.html#T26" target="_self">Th26</a>, <a class="ref" href="tdgroup.html#D4">TDGROUP:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon">z1</font> = <font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font>, <font color="Maroon">z2</font> = <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> ;<br/><a NAME="E9:72_1_1_1"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="afvect0.html#K3" target="_self">Padd</a> <font color="Maroon">o</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="afvect0.html#K3" target="_self">Padd</a> <font color="Maroon">o</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> )
 ;<br/><a NAME="E10:72_1_1_1"/><b>then </b>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">o</font>,<font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">o</font>,<font color="Maroon">x2</font>,<font color="Maroon">y1</font> )
 <b>by </b><i><a class="ref" href="afvect0.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E11:72_1_1_1"/><b>then </b>
( <font color="Maroon">o</font>,<font color="Maroon">x1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y2</font>,<font color="Maroon">z1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">z1</font> )
 <b>by </b><i><a class="ref" href="afvect0.html#T27" target="_self">Th27</a>, <a class="ref" href="afvect0.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E12:72_1_1_1"/><b>then </b>
<font color="Maroon">x1</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E13:72_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">AFV</font>
 <b>by </b><i><a class="ref" href="afvect0.html#T26" target="_self">Th26</a>, <a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:72_1_1_2"/><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">AFV</font>
 ;<br/><b>set </b><font color="Maroon">V</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font>;<br/><b>set </b><font color="Maroon">VV</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><a NAME="E2:72_1_1_2"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/><a NAME="E3:72_1_1_2"/><b>then </b><i><font color="Green">E112</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="afvect0.html#T24" target="_self">Th24</a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><a NAME="E4:72_1_1_2"/><b>then </b><i><font color="Green">E113</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font> &amp; <font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font> &amp; <font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font> &amp; <font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFV</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T10">MCART_1:10</a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/><b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">x2</font> = <font color="Maroon">x</font> <a href="mcart_1.html#K2">`2</a> , <font color="Maroon">y1</font> = <font color="Maroon">y</font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">y2</font> = <font color="Maroon">y</font> <a href="mcart_1.html#K2">`2</a>  as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> <b>by </b><i><a class="ref" href="afvect0.html#T25" target="_self">Th25</a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon">x1'</font> = <font color="Maroon">x1</font>, <font color="Maroon">x2'</font> = <font color="Maroon">x2</font>, <font color="Maroon">y1'</font> = <font color="Maroon">y1</font>, <font color="Maroon">y2'</font> = <font color="Maroon">y2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> ;<br/><a NAME="E7:72_1_1_2"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">x1</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font>
 <b>by </b><i><a class="ref" href="afvect0.html#T24" target="_self">Th24</a>, <a class="ref" href="afvect0.html#T26" target="_self">Th26</a>, <a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/><a NAME="E8:72_1_1_2"/>
<font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1_2_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">z1</font> = <font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font>, <font color="Maroon">z2</font> = <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFV</font> ;<br/>
<a NAME="E2:72_1_1_2_1"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="afvect0.html#K3" target="_self">Padd</a> <font color="Maroon">o</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="afvect0.html#K3" target="_self">Padd</a> <font color="Maroon">o</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> )
 
;<br/>
<a NAME="E3:72_1_1_2_1"/><b>then </b><i><font color="Green">E115</font></i>: 
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">o</font>,<font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">o</font>,<font color="Maroon">x2</font>,<font color="Maroon">y1</font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:72_1_1_2_1"/><b>then </b>
( <font color="Maroon">o</font>,<font color="Maroon">x1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y2</font>,<font color="Maroon">z1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">z2</font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:72_1_1_2_1"/><b>then </b>
( <font color="Maroon">x1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z1</font>,<font color="Maroon">y2</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">z2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:72_1_1_2_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">x2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y1</font>,<font color="Maroon">z1</font>
 
<b>by </b><i><a class="ref" href="afvect0.html#T27" target="_self">Th27</a>, </i>;<br/>
<b>hence </b><a NAME="E7:72_1_1_2_1"/>
<font color="Maroon">x1'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2'</font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">y1'</font>
 <b>by </b><i><a class="ref" href="afvect0.html#T28" target="_self">Th28</a>, <a class="ref" href="afvect0.html#T2" target="_self">Th2</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E9:72_1_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="tdgroup.html#K1">CONGRD</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>
 <b>by </b><i><a class="ref" href="afvect0.html#T26" target="_self">Th26</a>, <a class="ref" href="tdgroup.html#D4">TDGROUP:def 4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:72_1_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="tdgroup.html#K1">CONGRD</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> iff <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">AFV</font> )
 <b>by </b><i><a class="ref" href="afvect0.html#T23" target="_self">Th23</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:72_1"/>
 <a href="tdgroup.html#K1">CONGRD</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">AFV</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:72"/>
<font color="Maroon">AFV</font> <a href="hidden.html#R1">=</a>  <a href="tdgroup.html#K2">AV</a> <span class="p1">(<span class="default"><a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">AFV</font>,<font color="Maroon">o</font></span>)</span>
 <b>by </b><i><a class="ref" href="afvect0.html#T21" target="_self">Th21</a>, <a class="ref" href="tdgroup.html#T9">TDGROUP:9</a></i>;<br/>


</div>
