<?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="E1:7"/><i><font color="Green">E5</font></i>: 
 <a href="conaffm.html#NR5" target="_self">LIN_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="conaffm.html#D4" target="_self">CONAFFM:def 4</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="E2:7"/><i><font color="Green">E6</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>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <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>8</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R4">_|_</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>7</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; 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>3</sub></font> &amp; 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>5</sub></font> )
 ;<br/>

<a NAME="E3:7"/><i><font color="Green">E7</font></i>: 
 <a href="conaffm.html#NR6" target="_self">LIN1_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green">E5</font></i></a>, <a class="ref" href="conaffm.html#T3" target="_self">Th3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:7_1"/><i><font color="Green">E8</font></i>: 
 <a href="conaffm.html#NR5" target="_self">LIN_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>assume </b><a NAME="E2:7_1"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</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>12</sub></font> )
 ;<br/><b>assume </b><a NAME="E3:7_1"/><i><font color="Green">E10</font></i>: 
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><div><i><font color="Green">E11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:7_1_1"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_1_1"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_1_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_1_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E5:7_1_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E6:7_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_1_1"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_1_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_1_1"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_1_1"/>
not <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_1_2"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_1_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</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="E5:7_1_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_1_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E8:7_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_2"/><i><font color="Green">E13</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_1_2"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E3:7_1_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>9</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="7_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:7_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>9</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="7_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_2_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_1_2_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_2_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_2_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E7:7_1_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E8:7_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_1_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green">E13</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_1_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_1_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E11:7_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</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="E12:7_1_2"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_1_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_1_2"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green">E13</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E17:7_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_1_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E14:7_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_3"/><i><font color="Green">E14</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_1_3"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>10</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="7_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_3_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_1_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:7_1_3"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_3_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<a NAME="E2:7_1_3_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E6:7_1_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E7:7_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:7_1_3"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>11</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E5:7_1_3"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_1_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_3"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_1_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_1_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>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E11:7_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</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="E12:7_1_3"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_1_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_1_3"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_1_3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_1_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E17:7_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_1_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</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#D11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_1_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_1_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E14:7_1_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_4"/><i><font color="Green">E14</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_1_4"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</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>12</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>13</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>14</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>15</sub></font> &amp; <font color="Maroon">c<sub>10</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>15</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>9</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="7_1_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>9</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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:7_1_4_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</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="7_1_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_1_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_4_1_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_4_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E7:7_1_4_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E8:7_1_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_1_4_1"/>
<font color="Maroon">c<sub>9</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="7_1_4_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_3"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_1_3"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_4_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_4_1_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>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_1_4_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_4_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</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>12</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>13</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>14</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>15</sub></font> &amp; <font color="Maroon">c<sub>10</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>15</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:7_1_4"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_2"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>23</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:7_1_4_2"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</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>23</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<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="E5:7_1_4_2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>25</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_1_4_2"/>
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_2_1"/><b>then </b>
<font color="Maroon">c<sub>10</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>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_2"><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="E3:7_1_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:7_1_4_2"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>27</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E10:7_1_4_2"/><i><font color="Green">E18</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>27</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</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>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_1_4_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_1_4_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_1_4_2"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_1_4_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_1_4_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_1_4_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E19:7_1_4_2"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:7_1_4_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>28</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E15:7_1_4_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</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="E4:7_1_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:7_1_4_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>28</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_3"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_2_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>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:7_1_4_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_2_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>18</sub></font>,<font color="Maroon">c<sub>20</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="E4:7_1_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E22:7_1_4_2"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_1_4_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conaffm.html#E19:7_1_4_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conaffm.html#E20:7_1_4_2"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>23</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:7_1_4"/><i><font color="Green">E16</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>23</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E7:7_1_4"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_3"><b>proof </b></a><div class="add">

<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="E2:7_1_4_3"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</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#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:7_1_4_3"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>27</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>27</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_1_4_3"/><i><font color="Green">E19</font></i>: 
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_3_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:7_1_4_3"/>
not <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>11</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_3_2"/>
<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>11</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_3_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_4_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E7:7_1_4_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:7_1_4_3"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>29</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E11:7_1_4_3"/><i><font color="Green">E20</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>29</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>30</sub></font> = <font color="Maroon">c<sub>29</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <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="E13:7_1_4_3"/>
 <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>30</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:7_1_4_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:7_1_4_3"/><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>30</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:7_1_4_3"/><b>then </b>
<font color="Maroon">c<sub>9</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>13</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:7_1_4_3"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:7_1_4_3"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:7_1_4_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:7_1_4_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:7_1_4_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E20:7_1_4_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E21:7_1_4_3"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E16:7_1_4_3"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:7_1_4"/><i><font color="Green">E17</font></i>: 
(  <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>13</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>25</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E11:7_1_4"/><i><font color="Green">E18</font></i>: 
( <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>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>23</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_4"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_4"/><i><font color="Green">E19</font></i>: 
<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>9</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_4_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</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#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_1_4_4_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_1_4_4_1"/>
<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>13</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:7_1_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</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/>
<b>hence </b><a NAME="E10:7_1_4_4_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_4_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:7_1_4_4"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</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="7_1_4_4_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_4_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</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="E4:7_1_4_4_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_4_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_1_4_4"/>
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_4_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_4_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_4_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>21</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_4_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_1_4_4_3"/><b>then </b>
 <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>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_4_4_3"/><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>15</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_1_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_4_4_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_4_4"/>
( <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>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>23</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="txt" href="conaffm.html#E1:7_1_4_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4_4"><i><font color="Green">E20</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:7_1_4"/><i><font color="Green">E19</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_5"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_5"/><b>then </b>
<font color="Maroon">c<sub>9</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>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_4_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_4_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_1_4_5"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</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="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_1_4_5"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><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="E7:7_1_4_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_5"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:7_1_4"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_6"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_6"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_1_4_6"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_1_4_6"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_1_4_6"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_1_4_6"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_1_4_6"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_1_4_6"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_6"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_4_6"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>11</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="E14:7_1_4"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E15:7_1_4"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</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="txt" href="conaffm.html#E1:7_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conaffm.html#E13:7_1_4"><i><font color="Green">E20</font></i></a>, <a class="ref" href="conaffm.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E16:7_1_4"/><i><font color="Green">E22</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_7"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_1_4_7"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:7_1_4_7"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_1_4_7"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</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="E8:7_1_4_7"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:7_1_4_7"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:7_1_4_7"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_7"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:7_1_4_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:7_1_4_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E15:7_1_4_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:7_1_4"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_8"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_8"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:7_1_4_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</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="E6:7_1_4_8"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:7_1_4_8"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:7_1_4_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:7_1_4_8"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>25</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/>
<b>hence </b><a NAME="E12:7_1_4_8"/>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E6:7_1_4_8"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E18:7_1_4"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green">E7</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E15:7_1_4"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conaffm.html#E16:7_1_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self">Def6</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:7_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E6:7_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="conaffm.html#E7:7_1"><i><font color="Green">E13</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:7"/><b>then </b><i><font color="Green">E8</font></i>: 
( not <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>7</sub></font> implies <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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green">E5</font></i></a>, <a class="txt" href="conaffm.html#E2:7"><i><font color="Green">E6</font></i></a></i>;<br/>
<div><i><font color="Green">E9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:7_2"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</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>12</sub></font> )
 ;<br/><b>assume </b><a NAME="E2:7_2"/><i><font color="Green">E11</font></i>: 
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:7_2_1"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_2_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_2_1"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_1_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_2_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E5:7_2_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E6:7_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_2_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_2_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_2_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_2_1"/><b>then </b><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_2_1"/>
not <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_1_2"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_2_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</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="E5:7_2_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_2_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_2"/><i><font color="Green">E14</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_2_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E3:7_2_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>9</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="7_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:7_2_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</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="7_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_2_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_2_2_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_2_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_2_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E7:7_2_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E8:7_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_2_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_2_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_2_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E11:7_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</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="E12:7_2_2"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_2_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_2_2"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E17:7_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_2_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</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#D11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_2_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E14:7_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_3"/><i><font color="Green">E15</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_2_3"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>10</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="7_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_3_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_2_3_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_2_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:7_2_3"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_3_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<a NAME="E2:7_2_3_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E6:7_2_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E7:7_2_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:7_2_3"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>11</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="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E5:7_2_3"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_2_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_2_3"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_3"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</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#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_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>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E11:7_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</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="E12:7_2_3"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_2_3"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_2_3"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_2_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E17:7_2_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_2_3"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</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#D11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_2_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_2_3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E14:7_2_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_4"/><i><font color="Green">E15</font></i>: 
( not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</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> )
 ;<br/><a NAME="E2:7_2_4"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</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>12</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>14</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>13</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>15</sub></font> &amp; <font color="Maroon">c<sub>10</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>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</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>13</sub></font> &amp; <font color="Maroon">c<sub>10</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>15</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</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="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E2:7_2_4_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</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="7_2_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>9</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>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_2_4_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>9</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="7_2_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_1_2"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_4_1_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_4_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E7:7_2_4_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E8:7_2_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:7_2_4_1"/>
<font color="Maroon">c<sub>9</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="7_2_4_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_3"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_1_3"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_4_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_4_1_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>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_2_4_1_3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_2_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:7_2_4_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</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>12</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>14</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>13</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>15</sub></font> &amp; <font color="Maroon">c<sub>10</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>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</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>13</sub></font> &amp; <font color="Maroon">c<sub>10</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>15</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_4_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:7_2_4"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_2"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>23</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:7_2_4_2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>9</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>23</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>23</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>23</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>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="E5:7_2_4_2"/><i><font color="Green">E18</font></i>: 
( <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>25</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>25</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>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="E7:7_2_4_2"/>
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_2_1"/><b>then </b>
<font color="Maroon">c<sub>12</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>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:7_2_4_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:7_2_4_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_2_4_2_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</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="E6:7_2_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:7_2_4_2"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E10:7_2_4_2"/><i><font color="Green">E19</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>27</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>27</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>28</sub></font> = <font color="Maroon">c<sub>27</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_2_4_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_2"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_2_4_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</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="conaffm.html#E2:7_2_4_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_2_4_2"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_2_4_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_2_4_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_2_4_2"/><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>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E19:7_2_4_2"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:7_2_4_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E13:7_2_4_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:7_2_4_2"/><i><font color="Green">E24</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>28</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</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="E4:7_2_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E5:7_2_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:7_2_4_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>28</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_3"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>28</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:7_2_4_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_2_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>18</sub></font>,<font color="Maroon">c<sub>20</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="E4:7_2_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E23:7_2_4_2"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conaffm.html#E19:7_2_4_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conaffm.html#E20:7_2_4_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="conaffm.html#E21:7_2_4_2"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>23</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:7_2_4"/><i><font color="Green">E17</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>23</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>23</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="E7:7_2_4"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_3"><b>proof </b></a><div class="add">

<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="E2:7_2_4_3"/><i><font color="Green">E18</font></i>: 
( <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>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#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>27</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:7_2_4_3"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>27</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>27</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="E7:7_2_4_3"/>
not <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>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_3_1"/>
<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>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</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="txt" href="conaffm.html#E2:7_2_4_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>24</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>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_2_4_3_1"/><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>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analmetr.html#R4">_|_</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="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:7_2_4_3_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E9:7_2_4_3_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E10:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_4_3_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E11:7_2_4_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:7_2_4_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E16:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E17:7_2_4_3_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_4_3_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E18:7_2_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:7_2_4_3"/><b>then </b>
not <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>29</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E10:7_2_4_3"/><i><font color="Green">E20</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>29</sub></font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>28</sub></font>,<font color="Maroon">c<sub>29</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>30</sub></font> = <font color="Maroon">c<sub>29</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_2_4_3"/>
 <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>30</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_3"/><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>30</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_2_4_3"/><b>then </b>
<font color="Maroon">c<sub>9</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>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_2_4_3"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_2_4_3"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_2_4_3"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>27</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>30</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_2_4_3"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>30</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E19:7_2_4_3"/>
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="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_3"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:7_2_4"/><i><font color="Green">E18</font></i>: 
(  <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>11</sub></font> &amp; <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>25</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>26</sub></font> = <font color="Maroon">c<sub>25</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <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="E11:7_2_4"/><i><font color="Green">E19</font></i>: 
( <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>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>23</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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_4"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_4"/><i><font color="Green">E20</font></i>: 
<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>9</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_4_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</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="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_2_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_2_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_2_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>9</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>23</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_2_4_4_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<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>9</sub></font>,<font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_2_4_4_1"/>
<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>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_2_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:7_2_4_4_1"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:7_2_4_4_1"/><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>25</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E10:7_2_4_4_1"/>
<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>9</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4_4_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:7_2_4_4"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>9</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="7_2_4_4_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_4_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</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="E4:7_2_4_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_2_4_4"/>
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_4_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_4_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_2_4_4_3"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</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="E5:7_2_4_4_3"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</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="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_2_4_4_3"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_4"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conaffm.html#E4:7_2_4_4_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:7_2_4_4_3"/><b>then </b><i><font color="Green">E24</font></i>: 
<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>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:7_2_4_4_3"/>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E6:7_2_4_4_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:7_2_4_4_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>22</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:7_2_4_4_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>22</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="E12:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>22</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>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E14:7_2_4_4_3"/><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>10</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="E15:7_2_4_4_3"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E7:7_2_4_4_3"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E16:7_2_4_4_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_2_4_4"/>
( <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>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>23</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="txt" href="conaffm.html#E1:7_2_4_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_4"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E12:7_2_4"/><i><font color="Green">E20</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_5"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_5"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</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="E4:7_2_4_5"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</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="E5:7_2_4_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:7_2_4"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>23</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="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E14:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E15:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E16:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>9</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>23</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E17:7_2_4"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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="E18:7_2_4"/>
<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>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E19:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E20:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E21:7_2_4"/><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>25</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E22:7_2_4"/><b>then </b><i><font color="Green">E22</font></i>: 
 <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>25</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E23:7_2_4"/>
<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>26</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E24:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E25:7_2_4"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</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="E26:7_2_4"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green">E7</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E11:7_2_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_4"><i><font color="Green">E20</font></i></a>, <a class="txt" href="conaffm.html#E17:7_2_4"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conaffm.html#E22:7_2_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E27:7_2_4"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E28:7_2_4"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green">E7</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E11:7_2_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="conaffm.html#E17:7_2_4"><i><font color="Green">E21</font></i></a>, <a class="txt" href="conaffm.html#E22:7_2_4"><i><font color="Green">E22</font></i></a>, <a class="txt" href="conaffm.html#E25:7_2_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E29:7_2_4"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>25</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="7_2_4_6"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_6"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_6_1"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_6_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</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="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_6_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>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:7_2_4_6"/>
<font color="Maroon">c<sub>25</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="7_2_4_6_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_6_2"/>
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_6_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</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="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_6_2"/><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>9</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_6_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:7_2_4_6"/>
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>25</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="conaffm.html#E1:7_2_4_6"><i><font color="Green">E27</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E30:7_2_4"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E28:7_2_4"><i><font color="Green">E25</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E31:7_2_4"/><i><font color="Green">E28</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E32:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>24</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="E33:7_2_4"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E34:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>23</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E35:7_2_4"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E30:7_2_4"><i><font color="Green">E27</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E36:7_2_4"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_7"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<a NAME="E2:7_2_4_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</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="E3:7_2_4_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E37:7_2_4"/>
<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E31:7_2_4"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E38:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>24</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="E39:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E40:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E35:7_2_4"><i><font color="Green">E29</font></i></a>, <a class="txt" href="conaffm.html#E36:7_2_4"><i><font color="Green">E30</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E41:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>25</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>25</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E26:7_2_4"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E42:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>26</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E43:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E44:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E45:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E46:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>19</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>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E47:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>26</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E48:7_2_4"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>13</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="E49:7_2_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E31:7_2_4"><i><font color="Green">E28</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E50:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>24</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E51:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>24</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E52:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>12</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="E53:7_2_4"/><b>then </b>
<font color="Maroon">c<sub>25</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E26:7_2_4"><i><font color="Green">E24</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><b>hence </b><a NAME="E54:7_2_4"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E29:7_2_4"><i><font color="Green">E26</font></i></a>, <a class="txt" href="conaffm.html#E48:7_2_4"><i><font color="Green">E31</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:7_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conaffm.html#E6:7_2"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:7"/><b>then </b><i><font color="Green">E10</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>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> implies <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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7"><i><font color="Green">E6</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:7_3"/>
 <a href="conaffm.html#NR5" target="_self">LIN_holds_in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>assume </b><a NAME="E2:7_3"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; not <font color="Maroon">c<sub>9</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>12</sub></font> )
 ;<br/><b>assume </b><a NAME="E3:7_3"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><div><i><font color="Green">E13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:7_3_1"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_3_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_3_1"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_1_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E6:7_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_3_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_3_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_3_1"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_3_1"/><b>then </b><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_3_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_3_1"/>
not <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_1_2"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_3_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</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="E5:7_3_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_3_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_3_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="conaffm.html#E8:7_3_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_2"/><i><font color="Green">E15</font></i>: 
( <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>15</sub></font>,<font color="Maroon">c<sub>13</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> )
 ;<br/><a NAME="E2:7_3_2"/>
<font color="Maroon">c<sub>9</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="7_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<a NAME="E2:7_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:7_3_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:7_3_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E4:7_3_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><b>hence </b><a NAME="E5:7_3_2"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</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#T83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_3"/><i><font color="Green">E15</font></i>: 
( not <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>15</sub></font>,<font color="Maroon">c<sub>13</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> )
 ;<br/><a NAME="E2:7_3_3"/><i><font color="Green">E16</font></i>: 
( <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>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_3_3"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<a NAME="E2:7_3_3_1"/>
<font color="Maroon">c<sub>9</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="7_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:7_3_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_3_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</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="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_3_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</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="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:7_3_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_3_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_3_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</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="E8:7_3_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:7_3_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_3_3_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:7_3_3"/>
not <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>13</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_2"/><i><font color="Green">E18</font></i>: 
<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>13</sub></font>
 ;<br/>

<a NAME="E2:7_3_3_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>9</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="7_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:7_3_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_3_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</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="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_3_3_2_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</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="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:7_3_3_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:7_3_3_2_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</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/>
<b>hence </b><a NAME="E9:7_3_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:7_3_3_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green">E11</font></i></a>, <a class="txt" href="conaffm.html#E2:7_3_3_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:7_3_3"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7"><i><font color="Green">E9</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green">E15</font></i></a>, <a class="txt" href="conaffm.html#E2:7_3_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3_3"><i><font color="Green">E17</font></i></a></i>;<br/><b>hence </b><a NAME="E6:7_3_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</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#T83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:7_3"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_3"><i><font color="Green">E13</font></i></a>, <a class="txt" href="conaffm.html#E6:7_3"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:7"/>
<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>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green">E5</font></i></a>, <a class="txt" href="conaffm.html#E2:7"><i><font color="Green">E6</font></i></a>, <a class="txt" href="conaffm.html#E5:7"><i><font color="Green">E8</font></i></a>, <a class="txt" href="conaffm.html#E7:7"><i><font color="Green">E10</font></i></a></i>;<br/>


</div>
