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

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

<b>assume </b><a NAME="E1:19"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:19_1"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>12</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>11</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> )
 ;<br/><a NAME="E2:19_1"/><b>then </b><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E2:19_1_1_1"/><i><font color="Green">E20</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:19_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:19_1_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:19_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:19_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E7:19_1_1_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_1_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E4:19_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1_2"/><i><font color="Green">E19</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="E2:19_1_1_2"/><i><font color="Green">E20</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:19_1_1_2"/>
<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>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:19_1_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:19_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:19_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_1_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E7:19_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E4:19_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_1"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>(  <a href="aff_1.html#R1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> )
 ;<br/><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:19_1_2_1"/><i><font color="Green">E19</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="translac.html#T2">TRANSLAC:2</a></i>;<br/><a NAME="E4:19_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</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>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:19_1_2_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E7:19_1_2_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:19_1_2_1_1"/>
not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</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="E3:19_1_2_1_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:19_1_2_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</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="E6:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E8:19_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:19_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:19_1_2_1_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:19_1_2_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:19_1_2_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:19_1_2_1_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E10:19_1_2_1_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E13:19_1_2_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</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="E15:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E16:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:19_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:19_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>13</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E11:19_1_2_1_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_1.html#T52">AFF_1:52</a></i>;<br/>
<a NAME="E21:19_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="aff_1.html#R4">//</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E12:19_1_2_1_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E22:19_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:19_1_2_1_1"/><i><font color="Green">E21</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</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="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>15</sub></font>
;<br/>

<a NAME="E4:19_1_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:19_1_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:19_1_2_1_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:19_1_2_1"/><i><font color="Green">E21</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/><a NAME="E10:19_1_2_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:19_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E11:19_1_2_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_1_3"/><i><font color="Green">E24</font></i>: 
(  not <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> or  not <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> or  not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2_1_3_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> )
 ;<br/><a NAME="E2:19_1_2_1_3_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E3:19_1_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_1_3_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:19_1_2_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_1_3"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:19_1_2_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:19_1_2_1_4"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E9:19_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E2:19_1_2_1_4"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:19_1_2_1_4"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1_2_1_4"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_1_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:19_1_2_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E14:19_1_2_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E9:19_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr1.html#E10:19_1_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr1.html#E11:19_1_2_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr1.html#E12:19_1_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/><a NAME="E15:19_1_2_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:19_1_2_1_5"/>
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E9:19_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E2:19_1_2_1_5"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</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="E3:19_1_2_1_5"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1_2_1_5"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_1_5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E16:19_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E9:19_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr1.html#E10:19_1_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr1.html#E11:19_1_2_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/><b>hence </b><a NAME="E17:19_1_2_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E9:19_1_2_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conmetr1.html#E10:19_1_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr1.html#E11:19_1_2_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conmetr1.html#E14:19_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2_2"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>(  not  <a href="aff_1.html#R1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>3</sub></font> )
 ;<br/><a NAME="E2:19_1_2_2"/><i><font color="Green">E20</font></i>: 
 <a href="aff_1.html#R1">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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2_2_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:19_1_2_2_1"/><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E3:19_1_2_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_2_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_2_1_1"/><i><font color="Green">E25</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:19_1_2_2_1_1"/><i><font color="Green">E26</font></i>: 
 <a href="aff_1.html#R1">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="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>
<a NAME="E4:19_1_2_2_1_1"/>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:19_1_2_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E6:19_1_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_2_1_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:19_1_2_2_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_2_1"><i><font color="Green">E23</font></i></a></i>;<br/><a NAME="E5:19_1_2_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E6:19_1_2_2_1"/><b>then </b><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a></i>;<br/><a NAME="E7:19_1_2_2_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:19_1_2_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E8:19_1_2_2_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E4:19_1_2_2_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr1.html#E6:19_1_2_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2_2_2"/><i><font color="Green">E22</font></i>: 
<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="E2:19_1_2_2_2"/><i><font color="Green">E23</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E3:19_1_2_2_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_2_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:19_1_2_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:19_1_2_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:19_1_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:19_1_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E7:19_1_2_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:19_1_2_2_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_2_2"><i><font color="Green">E23</font></i></a></i>;<br/><a NAME="E5:19_1_2_2_2"/><i><font color="Green">E25</font></i>: 
 <a href="aff_1.html#R1">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="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E6:19_1_2_2_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_2_2_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:19_1_2_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1_2_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:19_1_2_2_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E5:19_1_2_2_2"><i><font color="Green">E25</font></i></a></i>;<br/><a NAME="E8:19_1_2_2_2"/><i><font color="Green">E27</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E9:19_1_2_2_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2_2_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1_2_2_2_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:19_1_2_2_2_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E3:19_1_2_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>6</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:19_1_2_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:19_1_2_2_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:19_1_2_2_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E8:19_1_2_2_2"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E11:19_1_2_2_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conmetr1.html#E7:19_1_2_2_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><a NAME="E12:19_1_2_2_2"/><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>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conmetr1.html#E4:19_1_2_2_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="conmetr1.html#E10:19_1_2_2_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E13:19_1_2_2_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:19_1_2_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:19_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conmetr1.html#E1:19_1_2_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conmetr1.html#E2:19_1_2_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conmetr1.html#E3:19_1_2_2"><i><font color="Green">E21</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:19_1_2"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:19_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:19_1"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:19"/>
<font color="Maroon">c<sub>1</sub></font> <a href="conmetr1.html#NR2" target="_self">satisfies_major_SCH</a> 
 <b>by </b><i><a class="ref" href="conmetr1.html#D2" target="_self">Def2</a></i>;<br/>


</div>
