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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="analoaf.html#V1">strict</a> <a href="tdgroup.html#NM3">AffVect</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="afvect0.html#K5" target="_self">GroupVect</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:72"/><i><font color="Green">E45</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span>;<br/><div><i><font color="Green">E46</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">E47</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><b>set </b><font color="Maroon">c<sub>7</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>4</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></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">E48</font></i>: 
( <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72_1_1_1"><i><font color="Green">E47</font></i></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">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> , <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="txt" href="afvect0.html#E3:72_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>12</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/><b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>12</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>11</sub></font>;<br/><a NAME="E7:72_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72_1_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="afvect0.html#E4:72_1_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="tdgroup.html#D4">TDGROUP:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/><a NAME="E9:72_1_1_1"/>
( <font color="Maroon">c<sub>19</sub></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">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>20</sub></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">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 ;<br/><a NAME="E10:72_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="ref" href="afvect0.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E11:72_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="afvect0.html#E7:72_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="afvect0.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E12:72_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="afvect0.html#T13" target="_self">Th13</a></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="afvect0.html#E4:72_1_1_1"><i><font color="Green">E49</font></i></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">E47</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>
 ;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>4</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></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">E48</font></i>: 
( <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72_1_1_2"><i><font color="Green">E47</font></i></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">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>5</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></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">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> , <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K1">`1</a> , <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="mcart_1.html#K2">`2</a>  as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="afvect0.html#E3:72_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="mcart_1.html#T10">MCART_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>12</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/><a NAME="E7:72_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="afvect0.html#E4:72_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analoaf.html#D2">ANALOAF:def 2</a></i>;<br/><a NAME="E8:72_1_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>15</sub></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">c<sub>17</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>14</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>15</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E2:72_1_1_2_1"/>
( <font color="Maroon">c<sub>17</sub></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">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>18</sub></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">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 
;<br/>
<a NAME="E3:72_1_1_2_1"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a>  <a href="afvect0.html#K2" target="_self">Padd</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E4:72_1_1_2_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:72_1_1_2_1"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="afvect0.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E6:72_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="afvect0.html#E7:72_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="afvect0.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E7:72_1_1_2_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="tdgroup.html#NK1" target="_self">#</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="afvect0.html#E3:72_1_1_2_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="afvect0.html#D5" target="_self">Def5</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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="afvect0.html#E4:72_1_1_2"><i><font color="Green">E49</font></i></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> iff <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72_1_1"><i><font color="Green">E46</font></i></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="afvect0.html#E1:72"><i><font color="Green">E45</font></i></a>, <a class="ref" href="tdgroup.html#T9">TDGROUP:9</a></i>;<br/>


</div>
