<?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><b>that </b><br/><a NAME="E1:15"/><i><font color="Green">E15</font></i>: 
 <a href="conmetr.html#NR1" target="_self">OPAP_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green">E16</font></i>: 
 <a href="conaffm.html#NR1" target="_self">DES_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#D2" target="_self">CONMETR:def 2</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><b>that </b><br/><a NAME="E3:15"/><i><font color="Green">E17</font></i>: 
( <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>and </b><br/><a NAME="E4:15"/><i><font color="Green">E18</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>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="E7:15"/><i><font color="Green">E19</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="txt" href="conmetr.html#E3:15"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:15"/><b>then </b><i><font color="Green">E20</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E21</font></i>: 
not <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:15_1_1"/><i><font color="Green">E24</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:15_1_1"/><i><font color="Green">E25</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="15_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_1_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="E4:15_1_1"/>
<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="15_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_1_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="15_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_1_2_1"/><i><font color="Green">E26</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="E2:15_1_1_2_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:15_1_1_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>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="E4:15_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_1_2_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_1_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="E5:15_1_1"/><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#E2:15_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E6:15_1_1"/><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#E1:15_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E7:15_1_1"/>
<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><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green">E24</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="E2:15_1_2"/><i><font color="Green">E25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:15_1_2"/><i><font color="Green">E26</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>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_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>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_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>15</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="E4:15_1_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>15</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_2"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E6:15_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</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="15_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_3"/><i><font color="Green">E25</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="E2:15_1_3"/><i><font color="Green">E26</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>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_3_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>17</sub></font>
 ;<br/>

<a NAME="E2:15_1_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>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="E3:15_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_3"/><i><font color="Green">E27</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_3_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</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/>


</div><b>end;</b></div><a NAME="E4:15_1_3"/>
<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>15</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E5:15_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4"/><i><font color="Green">E25</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>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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> )
 ;<br/><a NAME="E2:15_1_4"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</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> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:15_1_4_1_1"/><i><font color="Green">E30</font></i>: 
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>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_1_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>13</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_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>13</sub></font>,<font color="Maroon">c<sub>16</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="E3:15_1_4_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:15_1_4_1_1"/><i><font color="Green">E31</font></i>: 
 <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_1_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>14</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="E4:15_1_4_1_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_1_3"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_1_3"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</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="E5:15_1_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_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>
<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_2"/><i><font color="Green">E30</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="E2:15_1_4_1_2"/><i><font color="Green">E31</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="15_1_4_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_2_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="E2:15_1_4_1_2_1"/><b>then </b><i><font color="Green">E32</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:15_1_4_1_2_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_1_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>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="E5:15_1_4_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_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="E3:15_1_4_1_2"/><i><font color="Green">E32</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="15_1_4_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_2_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_2_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="E4:15_1_4_1_2"/>
<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="15_1_4_1_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_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>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E2:15_1_4_1_2_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="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_1_2_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><b>hence </b><a NAME="E5:15_1_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_1_3"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:15_1_4_1_3"/><i><font color="Green">E31</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="15_1_4_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_1_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="E2:15_1_4_1_3_1"/><b>then </b><i><font color="Green">E32</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:15_1_4_1_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_1_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="E5:15_1_4_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_3_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="E3:15_1_4_1_3"/><i><font color="Green">E32</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>14</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_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>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_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>14</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="E4:15_1_4_1_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>14</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_1_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_1_3_3"/>
<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>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_1_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>14</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="E5:15_1_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:15_1_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_1"><i><font color="Green">E29</font></i></a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/><b>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="E3:15_1_4_2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</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>20</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>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/><a NAME="E5:15_1_4_2"/>
 <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>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E7:15_1_4_2"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</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#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E9:15_1_4_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> holds <br/> <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>24</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="E1:15_1_4_2_1_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_2_1_1_1"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:15_1_4_2_1_1_1"/><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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_1_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:15_1_4_2_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>21</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/>
<b>hence </b><a NAME="E6:15_1_4_2_1_1_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</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="E2:15_1_4_2_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>24</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="E1:15_1_4_2_1_1_2"/><i><font color="Green">E34</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_2_1_1_2"/>
 <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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_4_2_1_1_2"/>
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15_1_4_2_1_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#D12">ANALMETR:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_2_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analmetr.html#R6">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T77">ANALMETR:77</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#D15">ANALMETR:def 15</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">c<sub>24</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E11:15_1_4_2"/><i><font color="Green">E32</font></i>: 
( <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>17</sub></font>,<font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E12:15_1_4_2"/>
not <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>26</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:15_1_4_2_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E4:15_1_4_2_2"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/>
<a NAME="E5:15_1_4_2_2"/>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E6:15_1_4_2_2"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#D4">AFF_1:def 4</a></i>;<br/>
<a NAME="E7:15_1_4_2_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>26</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:15_1_4_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>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E10:15_1_4_2_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<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>27</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_1_4_2_2"/>
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1_4_2_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E12:15_1_4_2_2"/><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>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_2_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_2_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E13:15_1_4_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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E14:15_1_4_2_2"/><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>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:15_1_4_2_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>16</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="E16:15_1_4_2_2"/><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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E17:15_1_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</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>25</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E14:15_1_4_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</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#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E16:15_1_4_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E17:15_1_4_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<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>17</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E19:15_1_4_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E20:15_1_4_2"/>
not <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_3"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_3"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</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#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>25</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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E19:15_1_4_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_2_3"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</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/>
<a NAME="E8:15_1_4_2_3"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_3_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_3_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<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>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E16:15_1_4_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_4_2_3_1"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_2_3_1"/><b>then </b>
<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>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_3_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E5:15_1_4_2_3_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E6:15_1_4_2_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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_2_3"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_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="E10:15_1_4_2_3"/>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>28</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E22:15_1_4_2"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>28</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E24:15_1_4_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E25:15_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E19:15_1_4_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E26:15_1_4_2"/><b>then </b><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>29</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E27:15_1_4_2"/><b>then </b><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>29</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>30</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E29:15_1_4_2"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>30</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E30:15_1_4_2"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_4"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_4"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</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#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_4"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>25</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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_2_4"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</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/>
<a NAME="E8:15_1_4_2_4"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_4_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_4_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<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>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:15_1_4_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E16:15_1_4_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_4_2_4_1"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_2_4_1"/><b>then </b>
<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>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_4_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E5:15_1_4_2_4_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E6:15_1_4_2_4_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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_2_4"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2_4"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_2_4"/>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_4"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_2_4"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>31</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E32:15_1_4_2"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>31</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>32</sub></font> = <font color="Maroon">c<sub>31</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E34:15_1_4_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E35:15_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E36:15_1_4_2"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>32</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E37:15_1_4_2"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>32</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E38:15_1_4_2"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</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>29</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>32</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_5"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> )
 ;<br/>

<div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2_5_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>
 ;<br/><a NAME="E2:15_1_4_2_5_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<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>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E17:15_1_4_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E3:15_1_4_2_5_1"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_4_2_5_1"/><b>then </b>
<font color="Maroon">c<sub>8</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#T48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_4_2_5_1"/><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>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E6:15_1_4_2_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>5</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E7:15_1_4_2_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>5</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:15_1_4_2_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>14</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E9:15_1_4_2_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_2_5_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> )
 ;<br/><a NAME="E2:15_1_4_2_5_2"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E26:15_1_4_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:15_1_4_2_5_2"/>
( <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_4_2_5_2"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E5:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E6:15_1_4_2_5_2"/><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>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E7:15_1_4_2_5_2"/><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>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:15_1_4_2_5_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>13</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/><a NAME="E9:15_1_4_2_5_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E10:15_1_4_2_5_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><a NAME="E11:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2_5_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/><a NAME="E12:15_1_4_2_5_2"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/><b>hence </b><a NAME="E13:15_1_4_2_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_2_5"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_5"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E39:15_1_4_2"/><i><font color="Green">E45</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_6"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> or  <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> )
 ;<br/>

<a NAME="E2:15_1_4_2_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>15</sub></font>,<font color="Maroon">c<sub>14</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E40:15_1_4_2"/><i><font color="Green">E46</font></i>: 
( 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>26</sub></font> &amp; not  <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>26</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_7"/>
(  <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>26</sub></font> or  <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>26</sub></font> )
 ;<br/>

<a NAME="E2:15_1_4_2_7"/><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>25</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</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/>
<a NAME="E3:15_1_4_2_7"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>18</sub></font> or <font color="Maroon">c<sub>25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_2_7"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_2_7"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2_7"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_2_7"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:15_1_4_2"/><i><font color="Green">E47</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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <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> &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>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_8"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_8"/>
( <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>11</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <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>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>15</sub></font> &amp; <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> &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> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_2_8"/><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>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp;  <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> &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>15</sub></font> &amp;  <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> &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> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_8"/>
(  <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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <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> &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>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E42:15_1_4_2"/><i><font color="Green">E48</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>29</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_9"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:15_1_4_2_9"/><b>then </b>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:15_1_4_2_9"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>28</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="E4:15_1_4_2_9"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>29</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="E43:15_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/><a NAME="E44:15_1_4_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</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="E45:15_1_4_2"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E42:15_1_4_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/><a NAME="E46:15_1_4_2"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</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="E47:15_1_4_2"/><i><font color="Green">E51</font></i>: 
not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_10"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_10"/>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_10"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_10"><i><font color="Green">E52</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_10"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E48:15_1_4_2"/>
not <font color="Maroon">c<sub>26</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="15_1_4_2_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_11"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_11"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_11"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_11"><i><font color="Green">E52</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_11"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E49:15_1_4_2"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E44:15_1_4_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E46:15_1_4_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="conmetr.html#E47:15_1_4_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E50:15_1_4_2"/><i><font color="Green">E53</font></i>: 
not  <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>32</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_12"/>
 <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>32</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_12"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_2_12"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>31</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_2_12"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_2_12"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_2_12"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_2_12"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E51:15_1_4_2"/><i><font color="Green">E54</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_13"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>28</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/>
<a NAME="E3:15_1_4_2_13"/>
<font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>28</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_13_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_13_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_13_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_13_1_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_13_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_13_1_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_13_1_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_13_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:15_1_4_2_13_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:15_1_4_2_13_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>31</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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:15_1_4_2_13_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:15_1_4_2_13_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>31</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E9:15_1_4_2_13_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E10:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_2_13_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E11:15_1_4_2_13_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_2_13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E22:15_1_4_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E47:15_1_4_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_2_13"><i><font color="Green">E55</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E52:15_1_4_2"/>
<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_2_14"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_2_14_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_2_14_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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_2_14_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E14:15_1_4_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_2_14_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_2_14_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_2_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_2_14"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_2_14"/>
<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E53:15_1_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#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E42:15_1_4_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E49:15_1_4_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="conmetr.html#E50:15_1_4_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conmetr.html#E51:15_1_4_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3"/><i><font color="Green">E28</font></i>: 
not <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/><b>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="E3:15_1_4_3"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</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>20</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>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/><a NAME="E5:15_1_4_3"/>
 <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>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E7:15_1_4_3"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</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#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E9:15_1_4_3"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E10:15_1_4_3"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_1_1"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> holds <br/> <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>24</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="E1:15_1_4_3_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_3_1_1_1"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:15_1_4_3_1_1_1"/><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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_1_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:15_1_4_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>21</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/>
<b>hence </b><a NAME="E6:15_1_4_3_1_1_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</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="E2:15_1_4_3_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>24</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="E1:15_1_4_3_1_1_2"/><i><font color="Green">E35</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_1_4_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>21</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_4_3_1_1_2"/>
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15_1_4_3_1_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#D12">ANALMETR:def 12</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_3_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analmetr.html#R6">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T77">ANALMETR:77</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#D15">ANALMETR:def 15</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">c<sub>24</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E12:15_1_4_3"/><i><font color="Green">E33</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>16</sub></font>,<font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E13:15_1_4_3"/>
not <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>26</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:15_1_4_3_2"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<a NAME="E4:15_1_4_3_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a></i>;<br/>
<a NAME="E5:15_1_4_3_2"/>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E6:15_1_4_3_2"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#D4">AFF_1:def 4</a></i>;<br/>
<a NAME="E7:15_1_4_3_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</sub></font>, <font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>26</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E9:15_1_4_3_2"/>
<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>25</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:15_1_4_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E10:15_1_4_3_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<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>27</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_1_4_3_2"/>
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1_4_3_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E15:15_1_4_3"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</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#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E17:15_1_4_3"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E18:15_1_4_3"/><b>then </b><i><font color="Green">E35</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>16</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E12:15_1_4_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E20:15_1_4_3"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E21:15_1_4_3"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_3"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_3"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</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#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>25</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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E20:15_1_4_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_3_3"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</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/>
<a NAME="E8:15_1_4_3_3"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_3_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_3_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<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>2</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_1_4_3_3_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_3_3_1"/><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#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_1_4_3_3_1"/><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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_3_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_1_4_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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:15_1_4_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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:15_1_4_3_3_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="E9:15_1_4_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_3_3"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_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="E10:15_1_4_3_3"/>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_3_3"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>28</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E23:15_1_4_3"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>29</sub></font> = <font color="Maroon">c<sub>28</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E25:15_1_4_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E26:15_1_4_3"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E20:15_1_4_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E27:15_1_4_3"/><b>then </b><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>29</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>30</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E29:15_1_4_3"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>30</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E30:15_1_4_3"/>
not <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_4"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_4"/>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/>
<a NAME="E4:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</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#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_4"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E5:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>25</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>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:15_1_4_3_4"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</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/>
<a NAME="E8:15_1_4_3_4"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_4_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_4_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<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>2</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_1_4_3_4_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_1_4_3_4_1"/><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#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_1_4_3_4_1"/><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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_4_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_1_4_3_4_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="E7:15_1_4_3_4_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="E8:15_1_4_3_4_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="E9:15_1_4_3_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:15_1_4_3_4"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3_4"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:15_1_4_3_4"/>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E11:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3_4"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E12:15_1_4_3_4"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E13:15_1_4_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>31</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E32:15_1_4_3"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>31</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T73">AFF_1:73</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>32</sub></font> = <font color="Maroon">c<sub>31</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E34:15_1_4_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E35:15_1_4_3"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E29:15_1_4_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E36:15_1_4_3"/><b>then </b><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>32</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E37:15_1_4_3"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>26</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>32</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>29</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_5"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> )
 ;<br/>

<div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3_5_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font>
 ;<br/><a NAME="E2:15_1_4_3_5_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E3:15_1_4_3_5_1"/><b>then </b>
<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>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E18:15_1_4_3"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_5_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E4:15_1_4_3_5_1"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:15_1_4_3_5_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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E6:15_1_4_3_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4_3_5_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font> )
 ;<br/><a NAME="E2:15_1_4_3_5_2"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E26:15_1_4_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E35:15_1_4_3"><i><font color="Green">E42</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E3:15_1_4_3_5_2"/>
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_5_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_5_2_1"/>
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:15_1_4_3_5_2_1"/>
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</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="E4:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E5:15_1_4_3_5_2"/><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>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E6:15_1_4_3_5_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E7:15_1_4_3_5_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>25</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E8:15_1_4_3_5_2"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E9:15_1_4_3_5_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><a NAME="E10:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_3_5_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/><a NAME="E11:15_1_4_3_5_2"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/><b>hence </b><a NAME="E12:15_1_4_3_5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_4_3_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1_4_3_5"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_5"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E38:15_1_4_3"/><i><font color="Green">E45</font></i>: 
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>26</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_6"/>
 <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>26</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_6"/><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>25</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_6"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_6"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_6"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_6"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_6"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E39:15_1_4_3"/><i><font color="Green">E46</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_7"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E40:15_1_4_3"/><i><font color="Green">E47</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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <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> &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>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_8"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_8"/>
( <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>11</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <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>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>15</sub></font> &amp; <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> &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> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E8:15"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_3_8"/><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>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp;  <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> &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>15</sub></font> &amp;  <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> &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> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_8"/>
(  <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>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <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> &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>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:15_1_4_3"/><i><font color="Green">E48</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>32</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_9"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_9"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>31</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E9:15_1_4_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:15_1_4_3_9"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>31</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="E3:15_1_4_3_9"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>32</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="E42:15_1_4_3"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E43:15_1_4_3"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E38:15_1_4_3"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E39:15_1_4_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/><a NAME="E44:15_1_4_3"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</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="E45:15_1_4_3"/><i><font color="Green">E50</font></i>: 
not  <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_10"/>
 <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>
 ;<br/>

<a NAME="E2:15_1_4_3_10"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E46:15_1_4_3"/><i><font color="Green">E51</font></i>: 
not  <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>26</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_11"/>
 <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>26</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</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/>
<a NAME="E3:15_1_4_3_11"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>25</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_11"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_11"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_11"><i><font color="Green">E52</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_11"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E47:15_1_4_3"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E48:15_1_4_3"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E45:15_1_4_3"><i><font color="Green">E50</font></i></a>, <a class="txt" href="conmetr.html#E46:15_1_4_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/><a NAME="E49:15_1_4_3"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</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="E50:15_1_4_3"/><i><font color="Green">E53</font></i>: 
not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_12"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_12"/>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_12"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_12"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_12"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E51:15_1_4_3"/>
not <font color="Maroon">c<sub>26</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="15_1_4_3_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_13"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_13"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_13"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_13"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_13"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E52:15_1_4_3"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E44:15_1_4_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E49:15_1_4_3"><i><font color="Green">E52</font></i></a>, <a class="txt" href="conmetr.html#E50:15_1_4_3"><i><font color="Green">E53</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E53:15_1_4_3"/><i><font color="Green">E55</font></i>: 
not  <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>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_14"/>
 <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>29</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_1_4_3_14"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>28</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:15_1_4_3_14"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E5:15_1_4_3_14"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1_4_3_14"><i><font color="Green">E56</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E6:15_1_4_3_14"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_4_3_14"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E54:15_1_4_3"/><i><font color="Green">E56</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_15"/><b>then </b><i><font color="Green">E57</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>31</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/>
<a NAME="E3:15_1_4_3_15"/>
<font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>31</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>31</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_15_1"/>
<font color="Maroon">c<sub>26</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="15_1_4_3_15_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_15_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_15_1_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</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="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_15_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_15_1_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_15_1_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_15_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_15_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</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="E5:15_1_4_3_15_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:15_1_4_3_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:15_1_4_3_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:15_1_4_3_15_1"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>28</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#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E9:15_1_4_3_15_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E10:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E8:15_1_4_3_15_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E11:15_1_4_3_15_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E12:15_1_4_3_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:15_1_4_3_15"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E23:15_1_4_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E32:15_1_4_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E2:15_1_4_3_15"><i><font color="Green">E57</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:15_1_4_3_15"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>
<a NAME="E6:15_1_4_3_15"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:15_1_4_3_15"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E8:15_1_4_3_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div><a NAME="E55:15_1_4_3"/>
<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4_3_16"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_4_3_16"/>
<font color="Maroon">c<sub>26</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="15_1_4_3_16_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_4_3_16_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:15_1_4_3_16_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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/>
<a NAME="E3:15_1_4_3_16_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:15"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E7:15_1_4_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E15:15_1_4_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E1:15_1_4_3_16_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E4:15_1_4_3_16_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_4_3_16_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:15_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E10:15_1_4_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:15_1_4_3_16"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E27:15_1_4_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E36:15_1_4_3"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_4_3_16"/>
<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E56:15_1_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#E2:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E37:15_1_4_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E40:15_1_4_3"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E41:15_1_4_3"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E52:15_1_4_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="conmetr.html#E53:15_1_4_3"><i><font color="Green">E55</font></i></a>, <a class="txt" href="conmetr.html#E54:15_1_4_3"><i><font color="Green">E56</font></i></a>, <a class="ref" href="conaffm.html#D1">CONAFFM:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_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#E3:15_1_4"><i><font color="Green">E27</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:15_1"/>
<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#E2:15_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E3:15_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E4:15_1"><i><font color="Green">E24</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:15"/>
<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#E1:15"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:15"><i><font color="Green">E18</font></i></a>, <a class="ref" href="conmetr.html#D1" target="_self">Def1</a></i>;<br/>


</div>
