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

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

<b>assume </b><a NAME="E1:16"/><i><font color="Green">E15</font></i>: 
 <a href="conmetr.html#NR3" target="_self">MH1_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:16"/><i><font color="Green">E16</font></i>: 
 <a href="conmetr.html#NR4" target="_self">MH2_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D1" target="_self">CONMETR:def 1</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

















<b>assume </b><a NAME="E3:16"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/>
<a NAME="E6:16"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<a NAME="E7:16"/><b>then </b><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>19</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:16"/><b>then </b><i><font color="Green">E19</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><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_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="E2:16_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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:16_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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_1"/><b>then </b><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>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_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="16_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_1_1"/>
<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="16_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_1_1_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="E2:16_1_1_1_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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:16_1_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>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="E4:16_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:16_1_1_1_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="E2:16_1_1_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>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_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="E3:16_1_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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E6:16_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#E2:16_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E4:16_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="E7:16_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#E1:16_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="E8:16_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="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_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="E2:16_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>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:16_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>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_1_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_2"/><b>then </b><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>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_1_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E6:16_1_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E7:16_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</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>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E2:16_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E4:16_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="E8:16_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="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_3"/><i><font color="Green">E24</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="E2:16_1_3"/><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>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_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>15</sub></font>
 ;<br/>

<a NAME="E2:16_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>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_1_3"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_3"/><b>then </b><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>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_1_3"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_1_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E6:16_1_3"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E7:16_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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E2:16_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E4:16_1_3"><i><font color="Green">E26</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="E5:16_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#E1:16_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E2:16_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E3:16_1"><i><font color="Green">E23</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green">E21</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="E2:16_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_1"/><i><font color="Green">E23</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="E2:16_2_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>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_1_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>13</sub></font>
 ;<br/>

<a NAME="E2:16_2_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:16_2_1_1"/>
<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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_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>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="E5:16_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_1"/>
<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>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_1"/><b>then </b><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>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:16_2_1"/>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <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="16_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2"/>
<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#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E2:16_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</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/>
<b>hence </b><a NAME="E3:16_2_1_2"/>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:16_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E4:16_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_2"/><i><font color="Green">E23</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<a NAME="E2:16_2_2"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>19</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E3:16_2_2"/><b>then </b>
( <font color="Maroon">c<sub>18</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:16_2_2"/><b>then </b>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:16_2_2"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_2"/><i><font color="Green">E26</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>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_2_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:16_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:16_2_2"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_2_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:16_2_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>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:16_2_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="E4:16_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:16_2_2"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E5:16_2_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E6:16_2_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><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="E5:16_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</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/><a NAME="E6:16_2"/><i><font color="Green">E25</font></i>: 
(  <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>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="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</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/><b>consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:16_2"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</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>22</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>23</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="E11:16_2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E12:16_2"/><i><font color="Green">E28</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_3"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</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="E3:16_2_3"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <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#E1:16_2_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>21</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>24</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:16_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E9:16_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>2</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>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_3"/><b>then </b>
<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>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_3"/><b>then </b>
<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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:16_2_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_3"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:16_2_3"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:16_2_3"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:16_2_3"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E13:16_2_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E18:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E20:16_2_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:16_2_3"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E22:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E23:16_2_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E24:16_2_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E20:16_2_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E25:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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/>
<a NAME="E26:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E27:16_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</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="E14:16_2"/>
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <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#E12:16_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>26</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E16:16_2"/><i><font color="Green">E29</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>26</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<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#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>26</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E18:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E16:16_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E19:16_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E20:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E16:16_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E21:16_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E22:16_2"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E9:16_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E23:16_2"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_4"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:16_2_4"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:16_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E19:16_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:16_2_4"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:16_2_4"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_4"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:16_2_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:16_2_4"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E5:16_2_4"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:16_2_4"/><b>then </b>
<font color="Maroon">c<sub>12</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>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:16_2_4"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_4"/><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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E12:16_2_4"/><b>then </b><i><font color="Green">E34</font></i>: 
<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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:16_2_4"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:16_2_4"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E15:16_2_4"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:16_2_4"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E12:16_2_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E17:16_2_4"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_4"/><b>then </b><i><font color="Green">E35</font></i>: 
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_4"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E21:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E22:16_2_4"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:16_2_4"/><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>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E19:16_2_4"><i><font color="Green">E35</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E24:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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/>
<a NAME="E25:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E26:16_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E24:16_2"/><b>then </b><i><font color="Green">E32</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>27</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>27</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E11:16_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E19:16_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E22:16_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>28</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E26:16_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</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>28</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>29</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="E28:16_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>29</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E29:16_2"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_5"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>28</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>29</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</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="E3:16_2_5"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16_2_5"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>26</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>30</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</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="E6:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E28:16_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E26:16_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>17</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="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_5"/><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>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:16_2_5"/><b>then </b><i><font color="Green">E37</font></i>: 
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_5"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:16_2_5"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_5"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</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#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E13:16_2_5"><i><font color="Green">E37</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E18:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:16_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>28</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>29</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="E31:16_2"/>
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E29:16_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>32</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E33:16_2"/><i><font color="Green">E36</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>32</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>33</sub></font> = <font color="Maroon">c<sub>32</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E35:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E33:16_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E36:16_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E37:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E33:16_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E38:16_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E39:16_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E26:16_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E40:16_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_6"/>
<font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:16_2_6"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E28:16_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E36:16_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_6"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:16_2_6"/><b>then </b>
<font color="Maroon">c<sub>2</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>27</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:16_2_6"/><b>then </b>
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:16_2_6"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</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="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_6"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:16_2_6"/><b>then </b>
<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>17</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/>
<a NAME="E8:16_2_6"/><b>then </b><i><font color="Green">E40</font></i>: 
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_6"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_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>11</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/>
<a NAME="E11:16_2_6"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_6"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</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#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E8:16_2_6"><i><font color="Green">E40</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E13:16_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>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:16_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:16_2"/><b>then </b><i><font color="Green">E39</font></i>: 
(  <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>33</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</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>33</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E28:16_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E36:16_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E39:16_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>34</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E43:16_2"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</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>34</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>35</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="E45:16_2"/><i><font color="Green">E41</font></i>: 
( <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>33</sub></font>,<font color="Maroon">c<sub>35</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>35</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E46:16_2"/><i><font color="Green">E42</font></i>: 
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_7"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>36</sub></font> = <font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>37</sub></font> = <font color="Maroon">c<sub>35</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</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="E3:16_2_7"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>36</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16_2_7"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>37</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>36</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>35</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E45:16_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E43:16_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_7"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_7"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_7"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_7"/><b>then </b>
 <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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E8:16_2_7"><i><font color="Green">E44</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E14:16_2_7"/><b>then </b>
<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>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:16_2_7"/><b>then </b><i><font color="Green">E45</font></i>: 
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E16:16_2_7"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_7"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_7"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:16_2_7"><i><font color="Green">E45</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E20:16_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E21:16_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>36</sub></font> = <font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>37</sub></font> = <font color="Maroon">c<sub>35</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="E48:16_2"/>
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>36</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>37</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E46:16_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>38</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E50:16_2"/><i><font color="Green">E43</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>38</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>37</sub></font>,<font color="Maroon">c<sub>38</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>39</sub></font> = <font color="Maroon">c<sub>38</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E52:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>35</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E50:16_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E53:16_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>35</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E54:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E50:16_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E55:16_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E56:16_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E43:16_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><b>take </b><font color="Maroon">c<sub>40</sub></font> = <font color="Maroon">c<sub>39</sub></font>;<br/><a NAME="E57:16_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>40</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_8"/>
<font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:16_2_8"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E45:16_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E53:16_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:16_2_8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:16_2_8"/><b>then </b>
<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:16_2_8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_8"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:16_2_8"/><b>then </b>
<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>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_8"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_8"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_8"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_8"/><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>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E8:16_2_8"><i><font color="Green">E47</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E13:16_2_8"/><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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:16_2_8"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E58:16_2"/><b>then </b><i><font color="Green">E46</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>40</sub></font> &amp; <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>33</sub></font>,<font color="Maroon">c<sub>40</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>40</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E45:16_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E53:16_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E56:16_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E59:16_2"/><i><font color="Green">E47</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9"/><i><font color="Green">E48</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:16_2_9"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_9_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_1"/>
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:16_2_9_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_9_1_1"/><b>then </b>
<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>21</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_9_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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_9_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</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="E6:16_2_9_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:16_2_9_1_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9_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>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/>
<a NAME="E9:16_2_9_1_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>11</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/>
<a NAME="E10:16_2_9_1_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_9_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<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>8</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="E12:16_2_9_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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_9_1_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>11</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/>
<a NAME="E14:16_2_9_1_1"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9_1_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>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_9_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_9_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_9_1_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="E18:16_2_9_1_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/>
<a NAME="E19:16_2_9_1_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>14</sub></font>,<font color="Maroon">c<sub>17</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="E20:16_2_9_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:16_2_9_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_2"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_9_1_2"/><b>then </b>
<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>26</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>26</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="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_9_1_2"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_9_1_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:16_2_9_1_2"/><b>then </b>
<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>26</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>26</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#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E5:16_2_9_1_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:16_2_9_1_2"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>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/>
<a NAME="E13:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_9_1_2"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9_1_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<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>8</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="E16:16_2_9_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_9_1_2"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_9_1_2"/><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>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:16_2_9_1_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:16_2_9_1_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:16_2_9_1_2"/><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="E22:16_2_9_1_2"/><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/>
<a NAME="E23:16_2_9_1_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>14</sub></font>,<font color="Maroon">c<sub>17</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="E24:16_2_9_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_9_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_3"/>
<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="E2:16_2_9_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_9_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16_2_9_1"/>
( <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</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> )
 <b>by </b><i><a class="txt" href="conmetr.html#E1:16_2_9_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_9_1"><i><font color="Green">E51</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16_2_9"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</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="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_9"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E10:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>12</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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</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="E12:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</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/>
<a NAME="E13:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>12</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>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_9"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>12</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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:16_2_9"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E15:16_2_9"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:16_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</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="E22:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</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="E23:16_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>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E24:16_2_9"/><b>then </b><i><font color="Green">E51</font></i>: 
<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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:16_2_9"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</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> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E26:16_2_9"/><b>then </b>
<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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E27:16_2_9"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E28:16_2_9"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E24:16_2_9"><i><font color="Green">E51</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E29:16_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>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E30:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E31:16_2_9"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E32:16_2_9"/><b>then </b><i><font color="Green">E52</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:16_2_9"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E34:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E35:16_2_9"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E36:16_2_9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E37:16_2_9"/><b>then </b>
<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>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E32:16_2_9"><i><font color="Green">E52</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E38:16_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</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="E39:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</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/>
<a NAME="E40:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E41:16_2_9"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E60:16_2"/><i><font color="Green">E48</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_10"/><i><font color="Green">E49</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>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:16_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:16_2_10"/><i><font color="Green">E50</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>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:16_2_10"/>
 <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>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E4:16_2_10"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_10"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_10"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E5:16_2_10"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:16_2_10"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:16_2_10"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_10"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_10"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E8:16_2_10"/><i><font color="Green">E53</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:16_2_10"/><i><font color="Green">E54</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_10"/>
 <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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E11:16_2_10"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E8:16_2_10"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conmetr.html#E9:16_2_10"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E12:16_2_10"/>
 <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>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_10"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E8:16_2_10"><i><font color="Green">E53</font></i></a>, <a class="txt" href="conmetr.html#E9:16_2_10"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E14:16_2_10"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E4:16_2_10"><i><font color="Green">E51</font></i></a>, <a class="txt" href="conmetr.html#E7:16_2_10"><i><font color="Green">E52</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_10"><i><font color="Green">E55</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E61:16_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>21</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E6:16_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E62:16_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<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>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E63:16_2"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E64:16_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>32</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E65:16_2"/><b>then </b>
<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>32</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E66:16_2"/><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>32</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E62:16_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E67:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E68:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E69:16_2"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E70:16_2"/><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>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E71:16_2"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E72:16_2"/>
 <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>26</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E73:16_2"/><b>then </b><i><font color="Green">E52</font></i>: 
<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>26</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E74:16_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E75:16_2"/>
 <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>38</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E76:16_2"/><b>then </b>
<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>38</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E77:16_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E73:16_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E78:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E79:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E80:16_2"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E81:16_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E82:16_2"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E83:16_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E63:16_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E84:16_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E71:16_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E85:16_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E74:16_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E86:16_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E82:16_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E87:16_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E88:16_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E89:16_2"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E90:16_2"/><i><font color="Green">E59</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11"/><i><font color="Green">E60</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:16_2_11"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:16_2_11_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1_1"/>
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:16_2_11_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_11_1_1"/><b>then </b>
<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>21</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_11_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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_11_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</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="E6:16_2_11_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E5:16_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:16_2_11_1_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_11_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>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/>
<a NAME="E9:16_2_11_1_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>11</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/>
<a NAME="E10:16_2_11_1_1"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_11_1_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<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>8</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="E12:16_2_11_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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_11_1_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>11</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/>
<a NAME="E14:16_2_11_1_1"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11_1_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>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_11_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_11_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_11_1_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="E18:16_2_11_1_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/>
<a NAME="E19:16_2_11_1_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>14</sub></font>,<font color="Maroon">c<sub>17</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="E20:16_2_11_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_11_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1_2"/>
<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="E2:16_2_11_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_11_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:16_2_11_1"/>
<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>20</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_11_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_11_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>12</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>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</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="E8:16_2_11_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>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/>
<a NAME="E9:16_2_11_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>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>12</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>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_11_1"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_11_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>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_11_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>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>12</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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2_11_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_11_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</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="E18:16_2_11_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>11</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="E19:16_2_11_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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E20:16_2_11_1"/><b>then </b><i><font color="Green">E66</font></i>: 
<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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:16_2_11_1"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</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> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:16_2_11_1"/><b>then </b>
<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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E23:16_2_11_1"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E24:16_2_11_1"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E20:16_2_11_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E25:16_2_11_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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E26:16_2_11_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>11</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/>
<a NAME="E27:16_2_11_1"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E28:16_2_11_1"/><b>then </b><i><font color="Green">E67</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E29:16_2_11_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>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E30:16_2_11_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>11</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/>
<a NAME="E31:16_2_11_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E32:16_2_11_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:16_2_11_1"/><b>then </b>
<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>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E28:16_2_11_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E34:16_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</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="E35:16_2_11_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>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/>
<a NAME="E36:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E37:16_2_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_11"/><i><font color="Green">E62</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E60:16_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_11"/><i><font color="Green">E63</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E60:16_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_11"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16_2_11"><i><font color="Green">E60</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:16_2_11"/><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>38</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:16_2_11"><i><font color="Green">E61</font></i></a>, <a class="txt" href="conmetr.html#E3:16_2_11"><i><font color="Green">E62</font></i></a>, <a class="txt" href="conmetr.html#E4:16_2_11"><i><font color="Green">E63</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E8:16_2_11"/><b>then </b><i><font color="Green">E64</font></i>: 
<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>38</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:16_2_11"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_11"/><b>then </b><i><font color="Green">E65</font></i>: 
<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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_11"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<a NAME="E2:16_2_11_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>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_11_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:16_2_11"/><b>then </b>
<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>38</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:16_2_11"><i><font color="Green">E64</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_11"><i><font color="Green">E65</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E14:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</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/>
<a NAME="E16:16_2_11"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_11"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>40</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>40</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:16_2_11"/><b>then </b>
<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>38</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E19:16_2_11"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>38</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#T13">AFF_1:13</a></i>;<br/>
<a NAME="E20:16_2_11"/><b>then </b>
<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>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E16:16_2_11"><i><font color="Green">E66</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E21:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E22:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E23:16_2_11"/><b>then </b><i><font color="Green">E67</font></i>: 
<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>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E24:16_2_11"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E26:16_2_11"/><b>then </b>
<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="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E27:16_2_11"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E23:16_2_11"><i><font color="Green">E67</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E28:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E29:16_2_11"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E91:16_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>40</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_12"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>40</sub></font>
 ;<br/>

<a NAME="E2:16_2_12"/><b>then </b><i><font color="Green">E61</font></i>: 
<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>27</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:16_2_12"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_12_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_12_1"/>
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:16_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_12_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E59:16_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:16_2_12"/><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>8</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_12"><i><font color="Green">E61</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:16_2_12"/><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="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:16_2_12"/><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="E7:16_2_12"/><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="E8:16_2_12"/><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="E9:16_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E92:16_2"/><i><font color="Green">E61</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>16</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E60:16_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>41</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="E94:16_2"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>41</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>41</sub></font> &amp; <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>41</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>41</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>42</sub></font> = <font color="Maroon">c<sub>41</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="E96:16_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>21</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="16_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_13"/>
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font>
 ;<br/>

<a NAME="E2:16_2_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E59:16_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">c<sub>43</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="E98:16_2"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>43</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>43</sub></font> &amp; <font color="Maroon">c<sub>38</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>43</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>43</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E92:16_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>44</sub></font> = <font color="Maroon">c<sub>43</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="E100:16_2"/><i><font color="Green">E65</font></i>: 
not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_14"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font>
 ;<br/>

<a NAME="E2:16_2_14"/>
<font color="Maroon">c<sub>41</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>41</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_14"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_14"><i><font color="Green">E66</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>32</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="E5:16_2_14"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E59:16_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E101:16_2"/><i><font color="Green">E66</font></i>: 
not <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_15"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font>
 ;<br/>

<a NAME="E2:16_2_15"/>
<font color="Maroon">c<sub>41</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>41</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_15"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>38</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_15"><i><font color="Green">E67</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_15"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>38</sub></font>,<font color="Maroon">c<sub>32</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="E5:16_2_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E90:16_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E102:16_2"/>
<font color="Maroon">c<sub>42</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>44</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_16"/>
<font color="Maroon">c<sub>41</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="conmetr.html#E96:16_2"><i><font color="Green">E63</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E2:16_2_16"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:16_2_16"/>
<font color="Maroon">c<sub>43</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>38</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E98:16_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E4:16_2_16"/><b>then </b>
<font color="Maroon">c<sub>44</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_16"/>
<font color="Maroon">c<sub>42</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>44</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E86:16_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E96:16_2"><i><font color="Green">E63</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_16"><i><font color="Green">E67</font></i></a>, <a class="ref" href="analmetr.html#T63">ANALMETR:63</a></i>;<br/>


</div><b>end;</b></div><a NAME="E103:16_2"/><b>then </b>
( <font color="Maroon">c<sub>42</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>44</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>44</sub></font> &amp; <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>44</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>44</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>44</sub></font> &amp; not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> &amp; not <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>42</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E92:16_2"><i><font color="Green">E61</font></i></a>, <a class="txt" href="conmetr.html#E94:16_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="conmetr.html#E96:16_2"><i><font color="Green">E63</font></i></a>, <a class="txt" href="conmetr.html#E98:16_2"><i><font color="Green">E64</font></i></a>, <a class="txt" href="conmetr.html#E100:16_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="conmetr.html#E101:16_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E104:16_2"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E87:16_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="conmetr.html#E88:16_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="conmetr.html#E89:16_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="conmetr.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E105:16_2"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_17"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</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#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E2:16_2_17"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:16_2_17_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>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_17_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_17"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:16_2_17"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_17_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:16_2_17_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_17_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:16_2_17"/>
( <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_17"><i><font color="Green">E69</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_17"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E3:16_2_17"><i><font color="Green">E71</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E106:16_2"/><i><font color="Green">E69</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:16_2_18"/><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>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:16_2_18"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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/>
<a NAME="E4:16_2_18"/>
 <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="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_18"/><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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:16_2_18"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:16_2_18"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_18_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>

<a NAME="E2:16_2_18_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>14</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_18_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:16_2_18"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</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#E3:16_2_18"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E6:16_2_18"><i><font color="Green">E71</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E9:16_2_18"/><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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:16_2_18"/><b>then </b><i><font color="Green">E72</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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_18"/><i><font color="Green">E73</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>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:16_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:16_2_18"/>
 <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>32</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E41:16_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_18"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E10:16_2_18"><i><font color="Green">E72</font></i></a>, <a class="txt" href="conmetr.html#E11:16_2_18"><i><font color="Green">E73</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>45</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>46</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>47</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>48</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>49</sub></font> = <font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>50</sub></font> = <font color="Maroon">c<sub>40</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E15:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:16_2_18"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>45</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_18"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>45</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_18"/>
<font color="Maroon">c<sub>48</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>46</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_18_2"/>
<font color="Maroon">c<sub>46</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font>
 ;<br/>

<a NAME="E2:16_2_18_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_18_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:16_2_18"/><b>then </b>
<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>47</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>45</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E16:16_2_18"><i><font color="Green">E75</font></i></a>, <a class="txt" href="conmetr.html#E19:16_2_18"><i><font color="Green">E76</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E22:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>45</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:16_2_18"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E24:16_2_18"/><i><font color="Green">E78</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>49</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E24:16_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E26:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>50</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E23:16_2_18"><i><font color="Green">E77</font></i></a>, <a class="txt" href="conmetr.html#E24:16_2_18"><i><font color="Green">E78</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E27:16_2_18"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E60:16_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E13:16_2_18"><i><font color="Green">E74</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>45</sub></font> = <font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>46</sub></font> = <font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>47</sub></font> = <font color="Maroon">c<sub>33</sub></font>, <font color="Maroon">c<sub>48</sub></font> = <font color="Maroon">c<sub>40</sub></font>, <font color="Maroon">c<sub>49</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>50</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>51</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>52</sub></font> = <font color="Maroon">c<sub>4</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="E108:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E106:16_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>53</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="E110:16_2"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">c<sub>53</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>45</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>53</sub></font> &amp; <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>53</sub></font> &amp; <font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>53</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>54</sub></font> = <font color="Maroon">c<sub>53</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="E112:16_2"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>45</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>47</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_19"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_19"/>
<font color="Maroon">c<sub>45</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>47</sub></font>
 ;<br/>

<a NAME="E2:16_2_19"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_19"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E59:16_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E113:16_2"/><i><font color="Green">E72</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>47</sub></font>,<font color="Maroon">c<sub>51</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E106:16_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E114:16_2"/><i><font color="Green">E73</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>50</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>52</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E106:16_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>55</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="E116:16_2"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">c<sub>55</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>46</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</sub></font> &amp; <font color="Maroon">c<sub>48</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</sub></font> &amp; <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>55</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>56</sub></font> = <font color="Maroon">c<sub>55</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="E118:16_2"/><i><font color="Green">E75</font></i>: 
not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_20"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_20"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font>
 ;<br/>

<a NAME="E2:16_2_20"/>
<font color="Maroon">c<sub>53</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>53</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_20"/><b>then </b>
<font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>46</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_20"><i><font color="Green">E76</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_20"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_20"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E59:16_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E119:16_2"/><i><font color="Green">E76</font></i>: 
not <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_21"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_21"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font>
 ;<br/>

<a NAME="E2:16_2_21"/>
<font color="Maroon">c<sub>53</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>53</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_21"/><b>then </b>
<font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>48</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_21"><i><font color="Green">E77</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_21"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_21"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E90:16_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E120:16_2"/>
<font color="Maroon">c<sub>54</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>56</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_22"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_22"/>
<font color="Maroon">c<sub>53</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E112:16_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E2:16_2_22"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>54</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:16_2_22"/>
<font color="Maroon">c<sub>55</sub></font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c<sub>46</sub></font>,<font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E116:16_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E4:16_2_22"/><b>then </b>
<font color="Maroon">c<sub>56</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>40</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_22"/>
<font color="Maroon">c<sub>54</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>56</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E86:16_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E112:16_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_22"><i><font color="Green">E77</font></i></a>, <a class="ref" href="analmetr.html#T63">ANALMETR:63</a></i>;<br/>


</div><b>end;</b></div><a NAME="E121:16_2"/><b>then </b>
( <font color="Maroon">c<sub>54</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>56</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>56</sub></font> &amp; not <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> &amp; not <font color="Maroon">c<sub>40</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>54</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E91:16_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="conmetr.html#E110:16_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="conmetr.html#E112:16_2"><i><font color="Green">E71</font></i></a>, <a class="txt" href="conmetr.html#E113:16_2"><i><font color="Green">E72</font></i></a>, <a class="txt" href="conmetr.html#E114:16_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="conmetr.html#E116:16_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="conmetr.html#E118:16_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="conmetr.html#E119:16_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E122:16_2"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E105:16_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="conmetr.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E123:16_2"/><b>then </b><i><font color="Green">E77</font></i>: 
( <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>8</sub></font>,<font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>40</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E104:16_2"><i><font color="Green">E67</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E124:16_2"/>
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>40</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_23"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_23"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>40</sub></font>
 ;<br/>

<a NAME="E2:16_2_23"/><i><font color="Green">E79</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:16_2_23"/><i><font color="Green">E80</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>45</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:16_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_23"/>
 <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>49</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>49</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/>
<a NAME="E6:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>45</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E2:16_2_23"><i><font color="Green">E79</font></i></a>, <a class="txt" href="conmetr.html#E3:16_2_23"><i><font color="Green">E80</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E7:16_2_23"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>45</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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:16_2_23"/>
 <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>48</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:16_2_23"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>48</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/>
<a NAME="E10:16_2_23"/><i><font color="Green">E83</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>48</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E12:16_2_23"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>48</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#E9:16_2_23"><i><font color="Green">E82</font></i></a>, <a class="ref" href="aff_1.html#T19">AFF_1:19</a></i>;<br/>
<a NAME="E13:16_2_23"/><b>then </b>
<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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E58:16_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E1:16_2_23"><i><font color="Green">E78</font></i></a>, <a class="txt" href="conmetr.html#E7:16_2_23"><i><font color="Green">E81</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E14:16_2_23"/><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>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_23"/><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>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:16_2_23"/><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>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_23"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E18:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E10:16_2_23"><i><font color="Green">E83</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_23"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_23"/><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>14</sub></font>,<font color="Maroon">c<sub>50</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E17:16_2_23"><i><font color="Green">E84</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E21:16_2_23"/><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>50</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E22:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>50</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="E23:16_2_23"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E125:16_2"/><b>then </b>
<font color="Maroon">c<sub>50</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>49</sub></font>,<font color="Maroon">c<sub>52</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E123:16_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E126:16_2"/><b>then </b>
<font color="Maroon">c<sub>50</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>52</sub></font>,<font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E127:16_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:16"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E9:16"><i><font color="Green">E20</font></i></a></i>;<br/>


</div>
