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

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

<b>assume </b><a NAME="E1:13"/><i><font color="Green">E15</font></i>: 
 <a href="conaffm.html#NR2" target="_self">AH_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#D5" target="_self">CONMETR:def 5</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>













<b>assume </b><a NAME="E2:13"/><i><font color="Green">E16</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>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>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>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <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>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <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>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:13"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</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>9</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</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="E6:13"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</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="E8:13"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<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>, <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#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="E10:13"/><i><font color="Green">E20</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>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:13_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>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:13_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:13_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_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>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:13_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:13_1"/><b>then </b>
<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>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E5:13_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:13_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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:13_1"/><b>then </b><i><font color="Green">E22</font></i>: 
 <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>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:13_1"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:13_1"/>
 <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>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E12:13_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E15:13_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:13_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:13_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E18:13_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:13_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E17:13_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E20:13_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E21:13_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:13_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:13_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E13:13_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr.html#E20:13_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>
<a NAME="E23:13_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>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="E24:13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</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="13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_2"/><i><font color="Green">E22</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:13_2"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 ;<br/>

<a NAME="E2:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E6:13"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:13"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</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="E9:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</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="E10:13_2_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_1"/>
 <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>16</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:13_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:13_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E16:13_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>22</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <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="E4:13_2"/><i><font color="Green">E23</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</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>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/><a NAME="E6:13_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:13_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E7:13_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:13_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E6:13"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E9:13_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E4:13_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E10:13_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E11:13_2"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E8:13"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</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="E13:13_2"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>24</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>24</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</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="E15:13_2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>9</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#D10">ANALMETR:def 10</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="E17:13_2"/>
not <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>19</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_2"/>
<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>19</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</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="E3:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E13:13_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E15:13_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:13_2_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>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_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>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:13_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:13_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>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="E9:13_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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="E14:13_2_2"/><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>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</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="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:13_2_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E18:13_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</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="E19:13_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>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>19</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="E21:13_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</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#E19:13_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E22:13_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</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="E23:13_2"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E13:13_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E24:13_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</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#E19:13_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E25:13_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</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="E26:13_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E15:13_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E27:13_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E28:13_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E29:13_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E30:13_2"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E31:13_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E26:13_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E32:13_2"/><i><font color="Green">E34</font></i>: 
not <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_3"/>
<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>
 ;<br/>

<a NAME="E2:13_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>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="E3:13_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>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="E4:13_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>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="E5:13_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:13_2_3"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_2_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_2_3"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:13_2_3"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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="E10:13_2_3"/><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>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:13_2_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:13_2_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</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="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:13_2_3"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E14:13_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E33:13_2"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_2_4"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:13_2_4"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:13_2_4"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:13_2_4"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:13_2_4"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_4"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:13_2_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:13_2_4"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E7:13_2_4"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:13_2_4"/><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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:13_2_4"/><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>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:13_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E34:13_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E27:13_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="conmetr.html#E30:13_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="conmetr.html#E31:13_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E32:13_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="conaffm.html#D2">CONAFFM:def 2</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>30</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="E36:13_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>30</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>30</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>31</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="E38:13_2"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>31</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>31</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D10">ANALMETR:def 10</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>32</sub></font> = <font color="Maroon">c<sub>30</sub></font>, <font color="Maroon">c<sub>33</sub></font> = <font color="Maroon">c<sub>31</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="E40:13_2"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_5"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>32</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>33</sub></font>
 ;<br/>

<a NAME="E2:13_2_5"/><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>9</sub></font>,<font color="Maroon">c<sub>31</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analmetr.html#R4">_|_</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#E36:13_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_5"/><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>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E38:13_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:13_2_5"/><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>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_5"/><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>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:13_2_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>18</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:13_2_5"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:13_2_5"/>
 <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>18</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E14:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:13_2_5"/><b>then </b><i><font color="Green">E39</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E10:13_2_5"><i><font color="Green">E38</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:13_2_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>14</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:13_2_5"/><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>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E19:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:13_2_5"/><b>then </b>
<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#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E15:13_2_5"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:13_2_5"/><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="E22:13_2_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>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="E23:13_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>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="E24:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E26:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E27:13_2_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E28:13_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>34</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="E42:13_2"/><i><font color="Green">E38</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>34</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>33</sub></font>,<font color="Maroon">c<sub>34</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>35</sub></font> = <font color="Maroon">c<sub>34</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="E44:13_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_6"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_6"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E42:13_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_2_6"/><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>2</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_6"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E36:13_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E45:13_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_7"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_7"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E42:13_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_2_7"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_7"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E38:13_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E46:13_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_8"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E47:13_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_9"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_9"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E48:13_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_10"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_10_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:13_2_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>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:13_2_10"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_10"/>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>


</div><b>end;</b></div><a NAME="E49:13_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_11"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_11_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:13_2_11"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:13_2_11"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_11"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:13_2_11"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_11"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:13_2_11"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_11"><i><font color="Green">E45</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E50:13_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E45:13_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E51:13_2"/><i><font color="Green">E46</font></i>: 
not <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>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_12"/>
<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>8</sub></font>
 ;<br/>

<a NAME="E2:13_2_12"/><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>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:13_2_12"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:13_2_12"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E8:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_12"/><b>then </b><i><font color="Green">E48</font></i>: 
<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>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E4:13_2_12"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E10:13_2_12"/>
<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>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:13_2_12"/><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>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E14:13_2_12"/><b>then </b>
<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#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E9:13_2_12"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:13_2_12"/><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="E16:13_2_12"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:13_2_12"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E20:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E21:13_2_12"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E22:13_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E52:13_2"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_13"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:13_2_13"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_2_13"/><b>then </b>
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_13"/><b>then </b>
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <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>15</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:13_2_13"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <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>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_13"/><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>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_13"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_13"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_2_13"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_13"/><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>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:13_2_13"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E14:13_2_13"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E16:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E17:13_2_13"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E13:13_2_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E18:13_2_13"/><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>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:13_2_13"/><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>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E20:13_2_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>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="E21:13_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E53:13_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conmetr.html#E44:13_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="conmetr.html#E46:13_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="conmetr.html#E47:13_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="conmetr.html#E48:13_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="conmetr.html#E49:13_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="conmetr.html#E50:13_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr.html#E51:13_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="conaffm.html#D2">CONAFFM:def 2</a></i>;<br/><a NAME="E54:13_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>35</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_14"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_14_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:13_2_14_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:13_2_14"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E34:13_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_14"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_14"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:13_2_14"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E5:13_2_14"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>35</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E10:13"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr.html#E53:13_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div><a NAME="E55:13_2"/><i><font color="Green">E49</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:13_2_15"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_2_15"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_2_15"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:13_2_15_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E11:13_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_15_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_15_1"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:13_2_15_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E6:13_2_15_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_2_15_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E3:13_2_15_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_2_15_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>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="E10:13_2_15_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>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="E11:13_2_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:13_2_15"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E8:13_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E3:13_2_15"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:13_2_15"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>29</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:13_2_15_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:13_2_15_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E31:13_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E1:13_2_15_2"><i><font color="Green">E52</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_15_2"/><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>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:13_2_15_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:13_2_15_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</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="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:13_2_15_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E8:13_2_15_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:13_2_15"/><b>then </b>
<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>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conmetr.html#E5:13_2_15"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:13_2_15"/><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>5</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E9:13_2_15"/><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>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:13_2_15"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:13_2_15"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_15_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_15_3"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:13_2_15_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>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_2_15_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:13_2_15"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E13:13_2_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>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E10:13_2_15"><i><font color="Green">E52</font></i></a>, <a class="txt" href="conmetr.html#E11:13_2_15"><i><font color="Green">E53</font></i></a>, <a class="ref" href="aff_1.html#T18">AFF_1:18</a></i>;<br/>
<b>hence </b><a NAME="E14:13_2_15"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E56:13_2"/><i><font color="Green">E50</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_16"/>
<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>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:13_2_16"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:13_2_16"/><b>then </b>
<font color="Maroon">c<sub>2</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>35</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E44:13_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:13_2_16"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>29</sub></font>,<font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:13_2_16"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E57:13_2"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_17"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_17"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>34</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E54:13_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:13_2_17"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div><a NAME="E58:13_2"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>28</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>34</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E55:13_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E56:13_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E59:13_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_18"><b>proof </b></a><div class="add">

<a NAME="E1:13_2_18"/>
<font color="Maroon">c<sub>9</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="13_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_2_18_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>29</sub></font>
 ;<br/>

<a NAME="E2:13_2_18_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E4:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr.html#E23:13_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:13_2_18_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_2_18_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>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_2_18_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:13_2_18_1"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:13_2_18_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E8:13_2_18_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13_2_18_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E10:13_2_18_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:13_2_18"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</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#E31:13_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="conmetr.html#E45:13_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="conmetr.html#E58:13_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:13_2_18"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</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="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:13_2_18"/><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>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:13_2_18"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E60:13_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3"/><i><font color="Green">E22</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:13_3"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E3:13_3"/><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>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E4:13_3"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:13_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:13_3"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E7:13_3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:13_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:13_3"/><i><font color="Green">E26</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>7</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:13_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>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:13_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:13_3"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E6:13_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr.html#E7:13_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E10:13_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E8:13_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E11:13_3"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E12:13_3"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E13:13_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</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/><a NAME="E14:13_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>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E15:13_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E16:13_3"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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="E17:13_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E18:13_3"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E19:13_3"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_3"/>
<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>5</sub></font>
 ;<br/><a NAME="E2:13_3_3"/><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>15</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E3:13_3_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E4:13_3_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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/><a NAME="E5:13_3_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:13_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E6:13_3_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E7:13_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr.html#E4:13_3_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_4"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:13_3_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E3:13_3_4"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E4:13_3_4"/><b>then </b>
<font color="Maroon">c<sub>15</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>17</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:13_3_4"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>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="E6:13_3_4"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conmetr.html#E8:13_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conmetr.html#E1:13_3_4"><i><font color="Green">E30</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="E22:13_3"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E16:13_3"><i><font color="Green">E27</font></i></a>, <a class="txt" href="conmetr.html#E19:13_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="conmetr.html#E20:13_3"><i><font color="Green">E29</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="E13:13"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr.html#E11:13"><i><font color="Green">E21</font></i></a></i>;<br/>


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