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

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

<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E15</font></i>: 
 <a href="conmetr.html#NR7" target="_self">OSCH_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E16</font></i>: 
 <a href="conmetr.html#NR5" target="_self">TDES_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#D6" target="_self">CONMETR:def 6</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



















<b>assume </b><b>that </b><br/><a NAME="E3:14"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 <b>and </b><br/><a NAME="E4:14"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/>
<a NAME="E7:14"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>21</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:14"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> implies ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:14_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<div><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1_1"/><i><font color="Green">E24</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>7</sub></font>
 ;<br/><a NAME="E2:14_1_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:14_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:14_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E5:14_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>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/><b>hence </b><a NAME="E6:14_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1_2"/><i><font color="Green">E25</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>9</sub></font>
 ;<br/><a NAME="E2:14_1_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>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:14_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E4:14_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</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/><b>hence </b><a NAME="E5:14_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_1_2"><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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1_3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:14_1_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E3:14_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:14_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:14_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E5:14_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>18</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E6:14_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_1_3"><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>
<b>hence </b><a NAME="E6:14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E3:14_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E4:14_1"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:14_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>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E8:14"><i><font color="Green">E20</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E3:14_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div>
<a NAME="E10:14"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> implies ( <font color="Maroon">c<sub>3</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>4</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> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_3"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:14_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>7</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_3_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:14_3_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>6</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:14_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E4:14_3_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>13</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E5:14_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_3_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:14_3_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:14_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:14_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</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/><a NAME="E5:14_3_2"/><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>15</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="E6:14_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_3_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:14_3_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:14_3_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>13</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="E4:14_3_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</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="E5:14_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_3"><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>
<b>hence </b><a NAME="E6:14_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E3:14_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E4:14_3"><i><font color="Green">E26</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E2:14_4_1"/><i><font color="Green">E26</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<a NAME="E2:14_4_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>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/>
<b>hence </b><a NAME="E3:14_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E10:14"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:14_4_1"/><i><font color="Green">E27</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_1_2"/>
<font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:14_4_1_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:14_4_1"/>
<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>19</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_1_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:14_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:14_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_1_3"/>
<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>19</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:14_4_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:14_4_2"/><i><font color="Green">E27</font></i>: 
not  <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>16</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_2_1"/>
 <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>16</sub></font>
 ;<br/>

<a NAME="E2:14_4_2_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>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="E3:14_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:14_4_2"/><i><font color="Green">E28</font></i>: 
 <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>18</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_2_2"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:14_4_2_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_2_2"/>
 <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>18</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:14_4_2"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_2_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:14_4_2_3"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_2_3"/>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:14_4_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>11</sub></font>
 ;<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="E3:14_4_3_1"/><i><font color="Green">E29</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>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> &amp; <font color="Maroon">c<sub>3</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="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="conmetr.html#T2" target="_self">Th2</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>22</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>24</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:14_4_3_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>24</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>25</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="E8:14_4_3_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>25</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>25</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="E10:14_4_3_1"/>
not <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_1"/>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:14_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:14_4_3_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:14_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:14_4_3_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:14_4_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:14_4_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<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="E7:14_4_3_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>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:14_4_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>28</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E12:14_4_3_1"/><i><font color="Green">E32</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>28</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</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>29</sub></font> = <font color="Maroon">c<sub>28</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E14:14_4_3_1"/><i><font color="Green">E33</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:14_4_3_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:14_4_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:14_4_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:14_4_3_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_3_1_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E15:14_4_3_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_3"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:14_4_3_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:14_4_3_1_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_3_1_3"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E8:14_4_3_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:14_4_3_1"/><i><font color="Green">E35</font></i>: 
(  <a href="conmetr.html#NR5" target="_self">TDES_holds_in</a> <font color="Maroon">c<sub>1</sub></font> implies  <a href="conmetr.html#NR8" target="_self">des_holds_in</a> <font color="Maroon">c<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_4"/>
 <a href="conmetr.html#NR5" target="_self">TDES_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_4"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR7" target="_self">satisfies_TDES</a> 
 
<b>by </b><i><a class="ref" href="conmetr.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E3:14_4_3_1_4"/><b>then </b>
 <a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T28">AFF_2:28</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_3_1_4"/>
 <a href="conmetr.html#NR8" target="_self">des_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="conmetr.html#T8" target="_self">Th8</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:14_4_3_1"/><i><font color="Green">E36</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_5"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_5"/><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>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:14_4_3_1_5"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:14_4_3_1_5"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:14_4_3_1_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E6:14_4_3_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1_5"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:14_4_3_1"/><i><font color="Green">E37</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_6"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_6"/><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>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_3_1_6"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:14_4_3_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_7"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:14_4_3_1_7"/><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>15</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_3_1_7"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</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="E20:14_4_3_1"/><i><font color="Green">E39</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>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_8"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E14:14_4_3_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:14_4_3_1_8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:14_4_3_1_8"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_1_8"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:14_4_3_1_8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:14_4_3_1_8"/>
<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>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1_8"><i><font color="Green">E41</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E21:14_4_3_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E16:14_4_3_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E17:14_4_3_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E18:14_4_3_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E19:14_4_3_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E22:14_4_3_1"/><i><font color="Green">E41</font></i>: 
not  <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>22</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_9"/>
 <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>22</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_9"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:14_4_3_1_9"/>
<font color="Maroon">c<sub>3</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="14_4_3_1_9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_9_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_9_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>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:14_4_3_1_9_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:14_4_3_1_9_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>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:14_4_3_1_9_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:14_4_3_1_9"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_3_1_9"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:14_4_3_1_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:14_4_3_1_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</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/>
<b>hence </b><a NAME="E7:14_4_3_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_1_9"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E23:14_4_3_1"/><i><font color="Green">E42</font></i>: 
not  <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>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_10"/>
 <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>4</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_10"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:14_4_3_1_10"/>
<font color="Maroon">c<sub>3</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="14_4_3_1_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_10_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_10_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>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:14_4_3_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:14_4_3_1_10_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>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:14_4_3_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_4_3_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_3_1_10"><i><font color="Green">E43</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E24:14_4_3_1"/><i><font color="Green">E43</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>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_11"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_11"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:14_4_3_1_11"/><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#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:14_4_3_1_11"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_3_1_11"/>
<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>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E25:14_4_3_1"/><i><font color="Green">E44</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>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_12"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_12"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:14_4_3_1_12"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</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#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:14_4_3_1_12"/><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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_3_1_12"/>
<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><a NAME="E26:14_4_3_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_13"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_13"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:14_4_3_1_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:14_4_3_1_13"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:14_4_3_1_13"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:14_4_3_1_13"/><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>3</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:14_4_3_1_13"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E20:14_4_3_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:14_4_3_1_13"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>29</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_13_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_13_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:14_4_3_1_13_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<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#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:14_4_3_1_13_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>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:14_4_3_1_13_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E6:14_4_3_1_13_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:14_4_3_1_13_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:14_4_3_1_13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E5:14_4_3_1_13_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:14_4_3_1_13"/>
 <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>28</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E14:14_4_3_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:14_4_3_1_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>28</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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:14_4_3_1_13"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:14_4_3_1_13"/><b>then </b>
<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</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="E12:14_4_3_1_13"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E13:14_4_3_1_13"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E6:14_4_3_1_13"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_1_13"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E27:14_4_3_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E28:14_4_3_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E16:14_4_3_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E22:14_4_3_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E23:14_4_3_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="conmetr.html#E24:14_4_3_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E25:14_4_3_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E26:14_4_3_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E29:14_4_3_1"/><i><font color="Green">E47</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_14"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_14"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:14_4_3_1_14"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>29</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_14_1"/>
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_14_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E20:14_4_3_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:14_4_3_1_14_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:14_4_3_1_14_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>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/>
<a NAME="E5:14_4_3_1_14_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>23</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:14_4_3_1_14_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E7:14_4_3_1_14_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:14_4_3_1_14_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:14_4_3_1_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_1_14_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:14_4_3_1_14"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:14_4_3_1_14"/><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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:14_4_3_1_14"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:14_4_3_1_14"/><b>then </b>
<font color="Maroon">c<sub>22</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>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:14_4_3_1_14"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_1_14"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1_14"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E9:14_4_3_1_14"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:14_4_3_1_14"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<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#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:14_4_3_1_14"/><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>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:14_4_3_1_14"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E13:14_4_3_1_14"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:14_4_3_1_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:14_4_3_1_14"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_1_14"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E30:14_4_3_1"/><i><font color="Green">E48</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_15"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_15"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</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="E3:14_4_3_1_15"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>29</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_1_15_1"/>
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_1_15_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E20:14_4_3_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:14_4_3_1_15_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:14_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>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/>
<a NAME="E5:14_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:14_4_3_1_15_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E7:14_4_3_1_15_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:14_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:14_4_3_1_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_1_15_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:14_4_3_1_15"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<a NAME="E5:14_4_3_1_15"/><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>15</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:14_4_3_1_15"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:14_4_3_1_15"/><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>22</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:14_4_3_1_15"/><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>22</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_1_15"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1_15"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E9:14_4_3_1_15"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:14_4_3_1_15"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:14_4_3_1_15"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:14_4_3_1_15"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E13:14_4_3_1_15"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:14_4_3_1_15"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>23</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/>
<b>hence </b><a NAME="E15:14_4_3_1_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_1_15"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E31:14_4_3_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_16"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_16"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:14_4_3_1_16"/><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>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:14_4_3_1_16"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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/>
<b>hence </b><a NAME="E4:14_4_3_1_16"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E32:14_4_3_1"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_1_17"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_1_17"/>
<font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:14_4_3_1_17"/><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>15</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:14_4_3_1_17"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:14_4_3_1_17"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E33:14_4_3_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E16:14_4_3_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E21:14_4_3_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E28:14_4_3_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr.html#E29:14_4_3_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E30:14_4_3_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr.html#E31:14_4_3_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2"/>
not <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:14_4_3_2"/><b>then </b>
not <font color="Maroon">c<sub>20</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <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="E4:14_4_3_2"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T72">AFF_1:72</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>22</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>24</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:14_4_3_2"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="ref" href="conmetr.html#T3" target="_self">Th3</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>24</sub></font> as   <a href="struct_0.html#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="E9:14_4_3_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="analmetr.html#NR6" target="_self">is_line</a> 
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/><a NAME="E10:14_4_3_2"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>21</sub></font> is <a href="aff_1.html#V1">being_line</a> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>26</sub></font> be   <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>;<br/><b>consider </b><font color="Maroon">c<sub>27</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="E2:14_4_3_2_1_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>21</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T63">AFF_1:63</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</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="E4:14_4_3_2_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R9">//</a> <font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="analmetr.html#T64">ANALMETR:64</a></i>;<br/><a NAME="E5:14_4_3_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>24</sub></font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">c<sub>28</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T73">ANALMETR:73</a></i>;<br/><b>then 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="E7:14_4_3_2_1_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>28</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T88">ANALMETR:88</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>30</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/><b>take </b><font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>30</sub></font>;<br/><b>thus </b><a NAME="E9:14_4_3_2_1_1"/>
( <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="aff_1.html#T54">AFF_1:54</a></i>;<br/></div><b>end;</b></div><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="E4:14_4_3_2_1"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:14_4_3_2_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>27</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_2_1"><i><font color="Green">E33</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>28</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E8:14_4_3_2_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_2_1"><i><font color="Green">E33</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>29</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="E10:14_4_3_2_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3_2_1"><i><font color="Green">E33</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>26</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>32</sub></font> = <font color="Maroon">c<sub>29</sub></font>, <font color="Maroon">c<sub>33</sub></font> = <font color="Maroon">c<sub>28</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E12:14_4_3_2_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>32</sub></font> &amp; <font color="Maroon">c<sub>23</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>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>30</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>31</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_2_1_2"/><i><font color="Green">E39</font></i>: 
(  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>32</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>30</sub></font> or  not <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>31</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>35</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>36</sub></font>, <font color="Maroon">c<sub>37</sub></font> be    <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>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:14_4_3_2_1_2_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>36</sub></font>,<font color="Maroon">c<sub>37</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>
 <b>and </b><br/><a NAME="E2:14_4_3_2_1_2_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>36</sub></font> &amp; <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>37</sub></font> )
 <b>and </b><br/><a NAME="E3:14_4_3_2_1_2_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; not <font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 ;<br/><b>assume </b><a NAME="E4:14_4_3_2_1_2_1"/>
<font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>35</sub></font>
 ;<br/><a NAME="E5:14_4_3_2_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>36</sub></font> <a href="aff_1.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_2_1_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_3_2_1_2_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="aff_1.html#T48">AFF_1:48</a></i>;<br/><b>hence </b><a NAME="E6:14_4_3_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_3_2_1_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_2_1_2_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="aff_1.html#T37">AFF_1:37</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:14_4_3_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1_2"><i><font color="Green">E39</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:14_4_3_2_1"/><i><font color="Green">E39</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="conmetr.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E14:14_4_3_2_1"/><i><font color="Green">E40</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>32</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>33</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E9:14_4_3_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="conmetr.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E15:14_4_3_2_1"/><i><font color="Green">E41</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>30</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<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="14_4_3_2_1_3"><b>proof </b></a><div class="add">

<div><i><font color="Green">E42</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 ;<br/><a NAME="E2:14_4_3_2_1_3_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>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E3:14_4_3_2_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:14_4_3_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E9:14_4_3_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E43</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1_3_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:14_4_3_2_1_3_2"/><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>13</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:14_4_3_2_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1_3_3"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E2:14_4_3_2_1_3_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>15</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:14_4_3_2_1_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_3_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1_3_4"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 ;<br/><a NAME="E2:14_4_3_2_1_3_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E3:14_4_3_2_1_3_4"/><b>then </b>
<font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E10:14"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:14_4_3_2_1_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E3:14"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E9:14_4_3_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_3_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_4_3_2_1_3_5"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:14_4_3_2_1_3_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>18</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:14_4_3_2_1_3_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E10:14"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:14_4_3_2_1_3"/>
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>30</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<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#E1:14_4_3_2_1_3"><i><font color="Green">E42</font></i></a>, <a class="txt" href="conmetr.html#E2:14_4_3_2_1_3"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4_3_2_1_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1_3"><i><font color="Green">E45</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:14_4_3_2_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_4"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E2:14_4_3_2_1_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E3:14_4_3_2_1_4"/>
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:14_4_3_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_5"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:14_4_3_2_1_5"/>
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</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/>


</div><b>end;</b></div><a NAME="E18:14_4_3_2_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E19:14_4_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E13:14_4_3_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E14:14_4_3_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E16:14_4_3_2_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="conmetr.html#E17:14_4_3_2_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E20:14_4_3_2_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E21:14_4_3_2_1"/>
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_6"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_6"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:14_4_3_2_1_6"/>
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:14_4_3_2_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E13:14_4_3_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E14:14_4_3_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E16:14_4_3_2_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E23:14_4_3_2_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_7"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="aff_1.html#T45">AFF_1:45</a></i>;<br/>
<a NAME="E2:14_4_3_2_1_7"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</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="E3:14_4_3_2_1_7"/>
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</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><a NAME="E24:14_4_3_2_1"/>
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_8"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:14_4_3_2_1_8"/>
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</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/>


</div><b>end;</b></div><a NAME="E25:14_4_3_2_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E13:14_4_3_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E14:14_4_3_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E15:14_4_3_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E23:14_4_3_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E26:14_4_3_2_1"/><i><font color="Green">E48</font></i>: 
( not <font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="aff_1.html#T49">AFF_1:49</a></i>;<br/><a NAME="E27:14_4_3_2_1"/>
( not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_9"><b>proof </b></a><div class="add">

<div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>34</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:14_4_3_2_1_9_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>34</sub></font> )
 ;<br/><b>assume </b><a NAME="E2:14_4_3_2_1_9_1"/>
<font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font>
 ;<br/><a NAME="E3:14_4_3_2_1_9_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1_9_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/><b>hence </b><a NAME="E4:14_4_3_2_1_9_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14_4_3_2_1_9_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/></div><b>end;</b></div>
<b>assume </b><a NAME="E2:14_4_3_2_1_9"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> or <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>24</sub></font> )
 ;<br/>

<b>hence </b><a NAME="E3:14_4_3_2_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1_9"><i><font color="Green">E49</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E28:14_4_3_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="conmetr.html#E20:14_4_3_2_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E22:14_4_3_2_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E25:14_4_3_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr.html#E26:14_4_3_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="conmetr.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E29:14_4_3_2_1"/><i><font color="Green">E50</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_3_2_1_10"><b>proof </b></a><div class="add">

<a NAME="E1:14_4_3_2_1_10"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>31</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="14_4_3_2_1_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_4_3_2_1_10_1"/>
not <font color="Maroon">c<sub>31</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:14_4_3_2_1_10_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E23:14_4_3_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:14_4_3_2_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:14_4_3_2_1_10_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>18</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:14_4_3_2_1_10_1"/><b>then </b>
<font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E10:14"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E6:14_4_3_2_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div>
<b>assume </b><a NAME="E2:14_4_3_2_1_10"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>4</sub></font> or  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E3:14_4_3_2_1_10"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>14</sub></font> or  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:14_4_3_2_1_10"/><b>then </b>
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> or <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>25</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E10:14_4_3_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="conmetr.html#E8:14_4_3_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1_10"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E5:14_4_3_2_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E10:14_4_3_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E1:14_4_3_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="aff_1.html#T30">AFF_1:30</a></i>;<br/>


</div><b>end;</b></div><a NAME="E30:14_4_3_2_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E23:14_4_3_2_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E31:14_4_3_2_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E6:14_4_3_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a></i>;<br/><b>hence </b><a NAME="E32:14_4_3_2_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E4:14_4_3_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E12:14_4_3_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="conmetr.html#E13:14_4_3_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E14:14_4_3_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E28:14_4_3_2_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E29:14_4_3_2_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="conmetr.html#E30:14_4_3_2_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E12:14_4_3_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:14"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:14"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conmetr.html#E7:14_4_3_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="conmetr.html#D7" target="_self">Def7</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:14_4_3"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4_3"><i><font color="Green">E27</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:14_4"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:14_4"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E3:14_4"><i><font color="Green">E25</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:14"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E9:14"><i><font color="Green">E21</font></i></a></i>;<br/>


</div>
