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<div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="analmetr.html#L1" target="_self">ParOrtStr</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="analmetr.html#V3" target="_self">OrtAfPl-like</a>
 ;<br/><a NAME="E2:64_1"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font> is   <a href="diraf.html#NM2">AffinPlane</a>
 <b>by </b><i><a class="ref" href="analmetr.html#D10" target="_self">Def10</a></i>;<br/><b>hence </b><a NAME="E3:64_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><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>, <font color="Maroon">c<sub>16</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/><a NAME="E5:64_1"/>
( <font color="Maroon">c<sub>17</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>17</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>hence </b><a NAME="E6:64_1"/>
( <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>9</sub></font> &amp; <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>11</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_1"/>
( <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>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <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>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> )
 ;<br/><a NAME="E2:64_1_1"/><b>then </b>
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><a NAME="E3:64_1_1"/><b>then </b>
( <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>23</sub></font>,<font color="Maroon">c<sub>24</sub></font> or <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>hence </b><a NAME="E4:64_1_1"/>
( <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_2"/>
<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>11</sub></font>
 ;<br/><a NAME="E2:64_1_2"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <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#T48" target="_self">Th48</a></i>;<br/><a NAME="E3:64_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>hence </b><a NAME="E4:64_1_2"/>
<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>11</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/></div>
<b>end;</b></div><b>consider </b><font color="Maroon">c<sub>25</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span><b> such that </b><br/><a NAME="E10:64_1"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>25</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>25</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</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 <font color="Maroon">c<sub>7</sub></font> ;<br/><a NAME="E12:64_1"/>
( <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>26</sub></font> &amp; <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>26</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E10:64_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E13:64_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <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="Olive">b<sub>1</sub></font> &amp; <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="Olive">b<sub>1</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>28</sub></font>, <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" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span><b> such that </b><br/><a NAME="E15:64_1"/><i><font color="Green">E54</font></i>: 
not <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>28</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>27</sub></font>,<font color="Maroon">c<sub>29</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>27</sub></font>, <font color="Maroon">c<sub>31</sub></font> = <font color="Maroon">c<sub>28</sub></font>, <font color="Maroon">c<sub>32</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>7</sub></font> ;<br/><a NAME="E17:64_1"/>
not <font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>31</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>30</sub></font>,<font color="Maroon">c<sub>32</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E15:64_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E18:64_1"/>
not for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> holds <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>
 ;<br/><b>consider </b><font color="Maroon">c<sub>33</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span><b> such that </b><br/><a NAME="E20:64_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>33</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>33</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>34</sub></font> = <font color="Maroon">c<sub>33</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><a NAME="E22:64_1"/>
( <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>34</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>34</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E20:64_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E23:64_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <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="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_3"/>
( <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>12</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>9</sub></font> )
 ;<br/><a NAME="E2:64_1_3"/><b>then </b>
( <font color="Maroon">c<sub>17</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> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>35</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:64_1_3"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>19</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>35</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>35</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>36</sub></font> = <font color="Maroon">c<sub>35</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><a NAME="E6:64_1_3"/>
( <font color="Maroon">c<sub>11</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>36</sub></font> &amp; <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>12</sub></font>,<font color="Maroon">c<sub>36</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E4:64_1_3"><i><font color="Green">E56</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E7:64_1_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>7</sub></font> st <br/>( <font color="Maroon">c<sub>11</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="Olive">b<sub>1</sub></font> &amp; <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>12</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/></div>
<b>end;</b></div><b>thus </b><a NAME="E25:64_1"/>
( ( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> implies <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> ) &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; ( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> implies ( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analmetr.html#R4" target="_self">_|_</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>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <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>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> &amp; not <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> implies <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> ) &amp; ( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> &amp; not <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> implies <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> ) &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</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="analmetr.html#E1:64_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="analmetr.html#D10" target="_self">Def10</a></i>;<br/><b>assume </b><a NAME="E26:64_1"/>
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>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 ;<br/><a NAME="E27:64_1"/><b>then </b>
not <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>35</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" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span><b> such that </b><br/><a NAME="E29:64_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>35</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>35</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E2:64_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>36</sub></font> = <font color="Maroon">c<sub>35</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><a NAME="E31:64_1"/>
( <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>36</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>36</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E29:64_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E32:64_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <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="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><a NAME="E2:64"/><i><font color="Green">E51</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>
 ;<br/>

<b>assume </b><a NAME="E3:64"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font>, <font color="Olive">b<sub>8</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> implies <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> ) &amp; ex <font color="Olive">b<sub>9</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>9</sub></font> ) &amp; not for <font color="Olive">b<sub>9</sub></font>, <font color="Olive">b<sub>10</sub></font>, <font color="Olive">b<sub>11</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> holds <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>10</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>11</sub></font> &amp; ex <font color="Olive">b<sub>9</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>9</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> implies ex <font color="Olive">b<sub>9</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>9</sub></font> ) ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> ) ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ex <font color="Olive">b<sub>9</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>9</sub></font> ) &amp; ( not <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies ex <font color="Olive">b<sub>9</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>9</sub></font> ) ) )
 ;<br/>

<a NAME="E4:64"/><i><font color="Green">E53</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:64"><i><font color="Green">E51</font></i></a></i>;<br/>
<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>now </b></a><div class="add"><b>let </b><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>, <font color="Maroon">c<sub>16</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>reconsider </b><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>16</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><b>thus </b><a NAME="E2:64_2"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>13</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:64_2_1"/>
( <font color="Maroon">c<sub>17</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>17</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:64_2_1"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E3:64_2"/>
( <font color="Maroon">c<sub>11</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>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> implies <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:64_2_2"/>
( <font color="Maroon">c<sub>11</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>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> )
 ;<br/>

<a NAME="E2:64_2_2"/><b>then </b>
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E3:64_2_2"/><b>then </b>
<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>20</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>22</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:64_2_2"/>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E4:64_2"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> implies <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>13</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:64_2_3"/>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E2:64_2_3"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <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#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E3:64_2_3"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:64_2_3"/>
<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>13</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:64"/><i><font color="Green">E55</font></i>: 
not for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> holds <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E2:64_3"/><i><font color="Green">E56</font></i>: 
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/>
<a NAME="E4:64_3"/>
not <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:64_3"><i><font color="Green">E56</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b><a NAME="E5:64_3"/>
not for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> holds <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>
 ;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E56</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E3:64_4"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/><a NAME="E5:64_4"/>
( <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>12</sub></font>,<font color="Maroon">c<sub>18</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>18</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64_4"><i><font color="Green">E57</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E6:64_4"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> st <br/>( <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>12</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E3:64_5"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</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" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/><a NAME="E5:64_5"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>18</sub></font> &amp; <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>12</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64_5"><i><font color="Green">E58</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E6:64_5"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <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>12</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_6"><b>now </b></a><div class="add"><b>let </b><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> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>assume </b><a NAME="E1:64_6"/><i><font color="Green">E59</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>11</sub></font>,<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>13</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>14</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>7</sub></font> ;<br/><a NAME="E3:64_6"/>
( <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:64_6"><i><font color="Green">E59</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>19</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E5:64_6"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/><a NAME="E7:64_6"/>
( <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>11</sub></font>,<font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E5:64_6"><i><font color="Green">E60</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E8:64_6"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> st <br/>( <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>11</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_7"><b>now </b></a><div class="add"><b>let </b><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> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>assume </b><a NAME="E1:64_7"/><i><font color="Green">E59</font></i>: 
not <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>14</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>7</sub></font> ;<br/><a NAME="E3:64_7"/>
not <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:64_7"><i><font color="Green">E59</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>19</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E5:64_7"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> ;<br/><a NAME="E7:64_7"/>
( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E5:64_7"><i><font color="Green">E60</font></i></a>, <a class="ref" href="analmetr.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E8:64_7"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Olive">b<sub>1</sub></font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:64"/>
 <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font>,the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">c<sub>7</sub></font> #) is   <a href="diraf.html#NM2">AffinPlane</a>
 <b>by </b><i><a class="txt" href="analmetr.html#E4:64"><i><font color="Green">E53</font></i></a>, <a class="txt" href="analmetr.html#E5:64"><i><font color="Green">E54</font></i></a>, <a class="txt" href="analmetr.html#E6:64"><i><font color="Green">E55</font></i></a>, <a class="txt" href="analmetr.html#E7:64"><i><font color="Green">E56</font></i></a>, <a class="txt" href="analmetr.html#E8:64"><i><font color="Green">E57</font></i></a>, <a class="txt" href="analmetr.html#E9:64"><i><font color="Green">E58</font></i></a>, <a class="ref" href="diraf.html#T54">DIRAF:54</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="analmetr.html#D10" target="_self">ANALMETR:def 10</a><br/>

<b>thus </b><a NAME="E12:64"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font>, <font color="Olive">b<sub>8</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> holds <br/>( ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> implies ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> ) ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> &amp; not <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> <a href="analoaf.html#R2">//</a> <font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>

<b>thus </b><a NAME="E13:64"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font>ex <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:64"><i><font color="Green">E52</font></i></a></i>;<br/>


</div>
