<?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="E1:17"/><i><font color="Green">E15</font></i>: 
 <a href="conaffm.html#NR3" target="_self">3H_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#D1" target="_self">CONMETR:def 1</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> 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>9</sub></font>, <font color="Maroon">c<sub>10</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="E2:17"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</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>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</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; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</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; <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</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>3</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>4</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>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>6</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> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>8</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>18</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>10</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="E5:17"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<a NAME="E6:17"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>19</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E7:17"/><b>then </b><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E8:17"/><i><font color="Green">E19</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  <a href="analmetr.html#R5">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> holds <br/>(  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>21</sub></font>, <font color="Maroon">c<sub>22</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_1"/><i><font color="Green">E20</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>21</sub></font>, <font color="Maroon">c<sub>25</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/>
<a NAME="E3:17_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:17_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:17_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>24</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>23</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>23</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="E5:17_1"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/><i><font color="Green">E21</font></i>: 
<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="E2:17_2"/><i><font color="Green">E22</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:17_2_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:17_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:17_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E5:17_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E2:17_2_1"><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="E3:17_2"/><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:17_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_3"/>
<font color="Maroon">c<sub>3</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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:17_2_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</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><b>hence </b><a NAME="E5:17_2"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E2:17_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E3:17_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><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_3"/><i><font color="Green">E22</font></i>: 
<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_3"/><i><font color="Green">E23</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<a NAME="E2:17_3_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:17_3_1"/>
<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>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:17_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:17_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E2:17_3_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:17_3"/><i><font color="Green">E24</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_3_2"/>
<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>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:17_3"/>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_3_3"/><i><font color="Green">E25</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:17_3_3"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:17_3_3"/><b>then </b>
<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>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_3_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:17_3_3"/>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <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#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:17_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E3:17_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E6:17_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E7:17_3"/>
<font color="Maroon">c<sub>3</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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4"/><i><font color="Green">E22</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> &amp; <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> )
 ;<br/><a NAME="E2:17_4"/><i><font color="Green">E23</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <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>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <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> &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; <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> &amp; <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>6</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> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <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>7</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</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="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_1"/><i><font color="Green">E24</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <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>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_1_1"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:17_4_1_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp;  <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> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</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="E3:17_4_1_1"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <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>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <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#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_4_1"/>
( not  <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>7</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_1_2"/>
(  <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>7</sub></font> or  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E2:17_4_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>16</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</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/>
<a NAME="E3:17_4_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>16</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</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="E4:17_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</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="E3:17_4_1"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <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>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <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> &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; <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> &amp; <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>6</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> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <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>7</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</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="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:17_4_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</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="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:17_4_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</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/><a NAME="E4:17_4_2"/>
 <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="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/><a NAME="E5:17_4_2"/><b>then </b><i><font color="Green">E27</font></i>: 
<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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:17_4_2"/><i><font color="Green">E28</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>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:17_4_2_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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:17_4_2"/>
<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>4</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:17_4_2"/><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>4</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E5:17_4_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E6:17_4_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E9:17_4_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E10:17_4_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a></i>;<br/><a NAME="E11:17_4_2"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<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#T55">ANALMETR:55</a></i>;<br/><a NAME="E12:17_4_2"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:17_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:17_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<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#E8:17"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E4:17_4_2_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_2_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E6:17_4_2_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>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_2_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</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="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_2_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E8:17_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:17_4_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:17_4_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E11:17_4_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E14:17_4_2"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3"/><i><font color="Green">E25</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>6</sub></font>
 ;<br/><a NAME="E2:17_4_3"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E3:17_4_3_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<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>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:17_4_3_1"/><i><font color="Green">E27</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>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<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#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:17_4_3_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>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E4:17_4_3_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_3_1_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</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="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E6:17_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</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="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</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="conmetr.html#E1:17_4_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E8:17_4_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E6:17_4_3_1"/><b>then </b>
<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>5</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="E7:17_4_3_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:17_4_3_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:17_4_3_1"/><i><font color="Green">E29</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>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:17_4_3_1"/>
 <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="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E10:17_4_3_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#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:17_4_3_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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:17_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E8:17_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:17_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</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/>
<a NAME="E13:17_4_3_1"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E14:17_4_3_1"/><i><font color="Green">E31</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:17_4_3_1"/>
 <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>2</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E16:17_4_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E17:17_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E13:17_4_3_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:17_4_3_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>20</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="E4:17_4_3"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>20</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">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:17_4_3_2"/><i><font color="Green">E29</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:17_4_3_2"/><i><font color="Green">E30</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<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="17_4_3_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:17_4_3_2"/>
<font color="Maroon">c<sub>14</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>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_2_2"/>
<font color="Maroon">c<sub>3</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_4_3_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_2_2_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_2_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E4:17_4_3_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_2_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_4_3_2_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_3_2_2"/>
<font color="Maroon">c<sub>14</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>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="E5:17_4_3_2"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E3:17_4_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E6:17_4_3_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E7:17_4_3_2"/>
<font color="Maroon">c<sub>3</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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3_3"/><i><font color="Green">E28</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>3</sub></font>
 ;<br/><a NAME="E2:17_4_3_3"/><i><font color="Green">E29</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>6</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E3:17_4_3_3_1"/><b>then </b>
<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>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:17_4_3_3_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>5</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="E5:17_4_3_3_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>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E6:17_4_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:17_4_3_3"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E3:17_4_3_3_2"/><b>then </b>
<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>6</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="E4:17_4_3_3_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</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>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_2"/><i><font color="Green">E31</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>6</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E4:17_4_3_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:17_4_3_3_2"/>
<font color="Maroon">c<sub>4</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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_3_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:17_4_3_3_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:17_4_3_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</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/>
<b>hence </b><a NAME="E9:17_4_3_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E8:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4"><i><font color="Green">E23</font></i></a></i>;<br/>


</div><b>end;</b></div><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="E5:17_4_3_3"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>22</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>6</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<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/><a NAME="E7:17_4_3_3"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>20</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>10</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1"/><i><font color="Green">E33</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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E2:17_4_3_3_3_1"/>
<font color="Maroon">c<sub>4</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="17_4_3_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_1_1"/><i><font color="Green">E35</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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="E3:17_4_3_3_3_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_3_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_3_1_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_3_1_1"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1_1_3"/>
<font color="Maroon">c<sub>14</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>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_3_1_1_3"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_4_3_3_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_3_1_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E3:17_4_3_3_3_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_3_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>20</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:17_4_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_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>8</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:17_4_3_3_3_1"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:17_4_3_3_3_1"/>
<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>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E8:17_4_3_3_3_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:17_4_3_3_3_1"/><b>then </b>
<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>6</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:17_4_3_3_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>7</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:17_4_3_3_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E12:17_4_3_3_3_1"/>
( <font color="Maroon">c<sub>20</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>10</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E6:17_4_3_3_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_4_3_3_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_3"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:17_4_3_3_3"/><i><font color="Green">E34</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_2"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>21</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/>
<a NAME="E3:17_4_3_3_3_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>21</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_2_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>21</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_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>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E3:17_4_3_3_3_2_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>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_2_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>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_3_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:17_4_3_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</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/>
<b>hence </b><a NAME="E7:17_4_3_3_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_3_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_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="E5:17_4_3_3_3_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:17_4_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</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="E7:17_4_3_3_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_3_3_2"><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>
<a NAME="E5:17_4_3_3_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_3"/><i><font color="Green">E35</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>6</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_3_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_3_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_3_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E4:17_4_3_3_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3_3_1"><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>
<a NAME="E2:17_4_3_3_3_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:17_4_3_3_3_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E5:17_4_3_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_3_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E5:17_4_3_3_3_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:17_4_3_3_3"/>
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:17_4_3_3_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_3_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:17_4_3_3"/>
not  <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>7</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_4"/>
 <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>7</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_4"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_3_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</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>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="E10:17_4_3_3"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E1:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<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/><a NAME="E12:17_4_3_3"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>24</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_1"/>
<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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E2:17_4_3_3_5_1"/><b>then </b>
<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>22</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_1"/><b>then </b>
<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>6</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:17_4_3_3_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>7</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_3_3_5_1"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:17_4_3_3_5_1"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</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="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E7:17_4_3_3_5_1"/><b>then </b>
<font color="Maroon">c<sub>24</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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E10:17_4_3_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:17_4_3_3_5_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>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E9:17_4_3_3_5_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>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E10:17_4_3_3_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E11:17_4_3_3_5_1"/>
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3_5_1"><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>
<a NAME="E2:17_4_3_3_5"/><i><font color="Green">E35</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_5_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_5"/><i><font color="Green">E36</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3"/><i><font color="Green">E37</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3_1"/><i><font color="Green">E40</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>6</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3_1_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E4:17_4_3_3_5_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_5_3_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_5_3_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_3_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_5_3_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_5_3_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:17_4_3_3_5_3_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>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E3:17_4_3_3_5_3_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:17_4_3_3_5_3_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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:17_4_3_3_5_3_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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:17_4_3_3_5_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</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/>
<b>hence </b><a NAME="E9:17_4_3_3_5_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_5_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3_3_5_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_3"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_5"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_5_3"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:17_4_3_3_5_3"/>
<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>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:17_4_3_3_5_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:17_4_3_3_5_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:17_4_3_3_5_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_5"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_4"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_4"/>
<font color="Maroon">c<sub>4</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_4_3_3_5_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_4_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_4_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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="E4:17_4_3_3_5_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_5_4_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E5:17_4_3_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:17_4_3_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E5:17_4_3_3_5_4"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_4_3_3_5"/>
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17_4_3_3_5"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E3:17_4_3_3_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:17_4_3_3"/>
<font color="Maroon">c<sub>20</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="17_4_3_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_6"/><i><font color="Green">E35</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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E3:17_4_3_3_6"/>
<font color="Maroon">c<sub>4</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="17_4_3_3_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_6_1"/><i><font color="Green">E37</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:17_4_3_3_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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="E3:17_4_3_3_6_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_6_1"/><i><font color="Green">E38</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_6_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_6_1_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_6_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</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/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_6_1"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_6_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_6_1_3"/>
<font color="Maroon">c<sub>14</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>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_6_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_6_1_3"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_4_3_3_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:17_4_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_6_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E3:17_4_3_3_6_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_6"/><b>then </b>
<font color="Maroon">c<sub>5</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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:17_4_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4_3_3_6"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E2:17_4_3_3_6"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:17_4_3_3_6"/><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>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:17_4_3_3_6"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_3_3_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</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/>
<b>hence </b><a NAME="E8:17_4_3_3_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:17_4"><i><font color="Green">E22</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="E14:17_4_3_3"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E4:17_4_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E7:17_4_3_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E10:17_4_3_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E12:17_4_3_3"><i><font color="Green">E33</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="E8:17_4_3"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E6:17_4_3"><i><font color="Green">E27</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_4"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E3:17_4"><i><font color="Green">E24</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:17"/>
<font color="Maroon">c<sub>3</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="conmetr.html#E9:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr.html#E10:17"><i><font color="Green">E21</font></i></a></i>;<br/>


</div>
