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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E15</font></i>: 
 <a href="conmetr.html#NR3" target="_self">MH1_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<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>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D7" target="_self">CONMETR:def 7</a><br/><b>let </b><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> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>assume </b><a NAME="E2:11"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</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>6</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>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<a NAME="E3:11"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i><a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>21</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:11"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E7:11"/>
not <font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 ;<br/>

<a NAME="E2:11_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E3:11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:11"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T72">AFF_1:72</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>22</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="E10:11"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>22</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:11_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:11_2_1"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:11_2_1"/><b>then </b>
<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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:11_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:11_2_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:11_2"/><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E4:11_2"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 ;<br/>

<a NAME="E2:11_2_2"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<b>hence </b><a NAME="E3:11_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:11_2"/>
<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>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:11_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E2:11_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E3:11_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_3"/><i><font color="Green">E21</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>9</sub></font>
 ;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_3_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:11_3_1"/><i><font color="Green">E24</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 ;<br/>

<a NAME="E2:11_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>16</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="E3:11_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:11_3_1"/><i><font color="Green">E25</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E4:11_3_1"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:11_3_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E2:11_3_1_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:11_3_1_2"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:11_3_1"/>
<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>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E2:11_3_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E3:11_3_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_3_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:11_3_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T32">AFF_1:32</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>24</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="E4:11_3_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>22</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>26</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E7:11_3_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T32">AFF_1:32</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>26</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>28</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="E10:11_3_2"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp; <font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>28</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E12:11_3_2"/>
not <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_1"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:11_3_2_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E10:11_3_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:11_3_2_1"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:11_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:11_3_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:11_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:11_3_2_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:11_3_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E3:11_3_2_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:11_3_2_1"/><i><font color="Green">E29</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>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_1_1"/>
<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="E2:11_3_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</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>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:11_3_2_1_1"/><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>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:11_3_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:11_3_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:11_3_2_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_1_2"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:11_3_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:11_3_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:11_3_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:11_3_2_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E11:11_3_2_1"/><b>then </b>
<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>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:11_3_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E8:11_3_2_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E12:11_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E13:11_3_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:11_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E15:11_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E9:11_3_2_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>30</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E14:11_3_2"/><i><font color="Green">E27</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>30</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>30</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>30</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E16:11_3_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:11_3_2_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E14:11_3_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:11_3_2_2"/><b>then </b>
<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:11_3_2_2"/><b>then </b>
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E4:11_3_2_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E10:11_3_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:11_3_2"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:11_3_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E14:11_3_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>32</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E19:11_3_2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>32</sub></font> &amp; <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T32">AFF_1:32</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>33</sub></font> = <font color="Maroon">c<sub>32</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>34</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="E22:11_3_2"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>34</sub></font> &amp; <font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>31</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>35</sub></font> = <font color="Maroon">c<sub>34</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E24:11_3_2"/>
not <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>35</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_3"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>35</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:11_3_2_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E22:11_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E4:11_3_2_3"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E22:11_3_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E2:11_3_2_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:11_3_2_3"/>
<font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E6:11_3_2_3"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E19:11_3_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E7:11_3_2_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>33</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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:11_3_2_3"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E19:11_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:11_3_2_3"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_3_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_3_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_2_3_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:11_3_2_3_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:11_3_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:11_3_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:11_3_2_3"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_3_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</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>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_2_3_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:11_3_2_3_2"/><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>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:11_3_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:11_3_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_2_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:11_3_2_3"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E12:11_3_2_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</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="conmetr.html#E8:11_3_2_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E9:11_3_2_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E13:11_3_2_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E14:11_3_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:11_3_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E16:11_3_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11_3_2_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>36</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E26:11_3_2"/><i><font color="Green">E31</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>36</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>35</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>36</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>37</sub></font> = <font color="Maroon">c<sub>36</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E28:11_3_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_4"><b>proof </b></a><div class="add">

<a NAME="E1:11_3_2_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E26:11_3_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:11_3_2_4"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:11_3_2_4"/><b>then </b>
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>37</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:11_3_2_4"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_4"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E22:11_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E6:11_3_2_4"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E22:11_3_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E29:11_3_2"/><b>then </b><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>37</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>31</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E19:11_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E26:11_3_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>38</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E31:11_3_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>38</sub></font> &amp; <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T32">AFF_1:32</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>39</sub></font> = <font color="Maroon">c<sub>38</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>40</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="E34:11_3_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>40</sub></font> &amp; <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>37</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>41</sub></font> = <font color="Maroon">c<sub>40</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E36:11_3_2"/>
not <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>38</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>41</sub></font>,<font color="Maroon">c<sub>36</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_5"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>38</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>41</sub></font>,<font color="Maroon">c<sub>36</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>39</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:11_3_2_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>39</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:11_3_2_5"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E34:11_3_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:11_3_2_5"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>39</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E31:11_3_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E6:11_3_2_5"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</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="conmetr.html#E31:11_3_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2_5"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:11_3_2_5"/><b>then </b>
<font color="Maroon">c<sub>3</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>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E8:11_3_2_5"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:11_3_2_5"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:11_3_2_5"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_3_2_5_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font>
 ;<br/>

<a NAME="E2:11_3_2_5_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:11_3_2_5_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:11_3_2_5_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:11_3_2_5_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:11_3_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:11_3_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:11_3_2_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:11_3"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:11_3_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E9:11_3_2_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>42</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E38:11_3_2"/><i><font color="Green">E35</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>42</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>41</sub></font>,<font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>42</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>43</sub></font> = <font color="Maroon">c<sub>42</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E40:11_3_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2_6"><b>proof </b></a><div class="add">

<a NAME="E1:11_3_2_6"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>42</sub></font>,<font color="Maroon">c<sub>41</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E38:11_3_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:11_3_2_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:11_3_2_6"/><b>then </b>
<font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>43</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:11_3_2_6"/><b>then </b>
<font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>37</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E5:11_3_2_6"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E34:11_3_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:11_3_2"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>43</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>37</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E31:11_3_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E38:11_3_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E42:11_3_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E17:11_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E29:11_3_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E41:11_3_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="conmetr.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E43:11_3_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E17:11_3_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E44:11_3_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E29:11_3_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E45:11_3_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E41:11_3_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E46:11_3_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>43</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E41:11_3_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/><a NAME="E47:11_3_2"/>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>43</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E2:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:11_3_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E17:11_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E29:11_3_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E41:11_3_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E43:11_3_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E44:11_3_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E45:11_3_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="conmetr.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E48:11_3_2"/>
<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>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E42:11_3_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E46:11_3_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:11_3"/>
<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>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:11_3"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:11"/>
<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>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E12:11"><i><font color="Green">E20</font></i></a></i>;<br/>


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