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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM2">AffinPlane</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>assume </b><a NAME="E1:17"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:17"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:17_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:17_1"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:17_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:17_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:17_2"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:17"/><i><font color="Green">E21</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:17_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:17_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:17_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:17_3"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:17"/><i><font color="Green">E22</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:17_4"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:17_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E4:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:17_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:17_4"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:17"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_5"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_5_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:17_5_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E3:17_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:17_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E5:17"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17_5"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_5_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><a NAME="E2:17_5_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E3:17_5_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:17_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E6:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:17_5"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:17"/><i><font color="Green">E24</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_6"><b>proof </b></a><div class="add">

<a NAME="E1:17_6"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E2:17_6"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:17"/><i><font color="Green">E25</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_7"/><i><font color="Green">E26</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:17_7"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:17_7"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E1:17_7"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>
<b>hence </b><a NAME="E4:17_7"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E1:17_7"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8"/><i><font color="Green">E26</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:17_8"/><i><font color="Green">E27</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_8_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E2:17_8_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E1:17_8"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>(  not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>1</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><a NAME="E2:17_8_2"/><b>then </b><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; not <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/><div><i><font color="Green">E31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:17_8_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E4:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E2:17_8"><i><font color="Green">E27</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><a NAME="E3:17_8_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E5:17"><i><font color="Green">E21</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="transgeo.html#T97">TRANSGEO:97</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8_2_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8_2_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:17_8_2_2_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E7:17"><i><font color="Green">E23</font></i></a>, <a class="txt" href="translac.html#E8:17"><i><font color="Green">E24</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E3:17_8_2_2_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E2:17_8_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="translac.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E4:17_8_2_2_1"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:17_8_2_2_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E4:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E2:17_8"><i><font color="Green">E27</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E6:17_8_2_2_1"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E5:17"><i><font color="Green">E21</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E7:17_8_2_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E2:17_8_2_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="translac.html#E4:17_8_2_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="translac.html#E5:17_8_2_2_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="transgeo.html#T97">TRANSGEO:97</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_8_2_2_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:17_8_2_2_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="translac.html#E7:17"><i><font color="Green">E23</font></i></a>, <a class="txt" href="translac.html#E8:17"><i><font color="Green">E24</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E3:17_8_2_2_2"/>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E4:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E2:17_8"><i><font color="Green">E27</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E4:17_8_2_2_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E9:17"><i><font color="Green">E25</font></i></a>, <a class="txt" href="translac.html#E2:17_8_2_2_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="transgeo.html#T97">TRANSGEO:97</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:17_8_2_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="translac.html#E2:17_8_2_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_8_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E1:17_8"><i><font color="Green">E26</font></i></a>, <a class="txt" href="translac.html#E1:17_8_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="translac.html#E3:17_8_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="translac.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_3"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:17_8_3"/><i><font color="Green">E29</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:17_8_3"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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>and </b><br/><a NAME="E4:17_8_3"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:17_8_3"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>and </b><br/><a NAME="E7:17_8_3"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E8:17_8_3"/><i><font color="Green">E34</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_8_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:17_8_3_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="translac.html#E1:17_8_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:17_8_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17_8_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E4:17_8_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:17_8_3"/><i><font color="Green">E35</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_8_3_2"/><i><font color="Green">E36</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:17_8_3_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:17_8_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="translac.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="translac.html#E1:17_8"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>
<b>hence </b><a NAME="E4:17_8_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E4:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="translac.html#E1:17_8"><i><font color="Green">E26</font></i></a>, <a class="txt" href="translac.html#E8:17_8_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="translac.html#E1:17_8_3_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T20">AFF_1:20</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:17_8_3"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_8_3_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_8_3_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:17_8_3_3"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="translac.html#E1:17_8_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:17_8_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E1:17_8_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>


</div><b>end;</b></div><a NAME="E11:17_8_3"/><b>then </b>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E3:17_8_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="translac.html#E4:17_8_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="translac.html#E6:17_8_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="translac.html#E7:17_8_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="translac.html#E8:17_8_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="translac.html#E9:17_8_3"><i><font color="Green">E35</font></i></a>, <a class="txt" href="translac.html#E16"><i><font color="Green">Lemma14</font></i></a></i>;<br/><b>hence </b><a NAME="E12:17_8_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_8"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E3:17_8"><i><font color="Green">E28</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:17"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="translac.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="translac.html#E16"><i><font color="Green">Lemma14</font></i></a></i>;<br/>


</div>
