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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E4</font></i>: 
not  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E5</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green">E6</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green">E7</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E6:16"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E7:16"/><i><font color="Green">E10</font></i>: 
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="pasch.html#E3:16"><i><font color="Green">E6</font></i></a>, <a class="txt" href="pasch.html#E4:16"><i><font color="Green">E7</font></i></a>, <a class="ref" href="diraf.html#T36">DIRAF:36</a></i>;<br/>
<a NAME="E8:16"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="pasch.html#E1:16"><i><font color="Green">E4</font></i></a>, <a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/>
<div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="pasch.html#E5:16"><i><font color="Green">E8</font></i></a>, <a class="txt" href="pasch.html#E6:16"><i><font color="Green">E9</font></i></a>, <a class="ref" href="diraf.html#T27">DIRAF:27</a></i>;<br/><a NAME="E3:16_1"/><i><font color="Green">E14</font></i>: 
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/><div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:16_1_1"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E7:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="pasch.html#E2:16_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="diraf.html#T39">DIRAF:39</a></i>;<br/><b>hence </b><a NAME="E3:16_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="pasch.html#E1:16"><i><font color="Green">E4</font></i></a>, <a class="txt" href="pasch.html#E7:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="pasch.html#E3:16_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pasch.html#E1:16_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:16_1_2"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E7:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="pasch.html#E2:16_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="diraf.html#T39">DIRAF:39</a></i>;<br/><b>hence </b><a NAME="E3:16_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="pasch.html#E1:16"><i><font color="Green">E4</font></i></a>, <a class="txt" href="pasch.html#E7:16"><i><font color="Green">E10</font></i></a>, <a class="txt" href="pasch.html#E3:16_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pasch.html#E1:16_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:16_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E4:16_1"><i><font color="Green">E15</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>assume </b><a NAME="E2:16_2"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E3:16_2"/><i><font color="Green">E15</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/><a NAME="E4:16_2"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E3:16"><i><font color="Green">E6</font></i></a>, <a class="txt" href="pasch.html#E4:16"><i><font color="Green">E7</font></i></a>, <a class="txt" href="pasch.html#E8:16"><i><font color="Green">E11</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><a NAME="E5:16_2"/>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/><a NAME="E6:16_2"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E3:16"><i><font color="Green">E6</font></i></a>, <a class="txt" href="pasch.html#E4:16"><i><font color="Green">E7</font></i></a>, <a class="txt" href="pasch.html#E8:16"><i><font color="Green">E11</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><a NAME="E7:16_2"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E5:16"><i><font color="Green">E8</font></i></a>, <a class="txt" href="pasch.html#E6:16"><i><font color="Green">E9</font></i></a>, <a class="txt" href="pasch.html#E8:16"><i><font color="Green">E11</font></i></a>, <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/><a NAME="E8:16_2"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#D5">DIRAF:def 5</a></i>;<br/><a NAME="E9:16_2"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T36">DIRAF:36</a></i>;<br/><a NAME="E10:16_2"/>
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="pasch.html#E3:16"><i><font color="Green">E6</font></i></a>, <a class="txt" href="pasch.html#E4:16"><i><font color="Green">E7</font></i></a>, <a class="txt" href="pasch.html#E8:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="pasch.html#E3:16_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="pasch.html#E8:16_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="diraf.html#T36">DIRAF:36</a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><a NAME="E11:16_2"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E2:16_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><a NAME="E12:16_2"/>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="diraf.html#T37">DIRAF:37</a></i>;<br/><a NAME="E13:16_2"/><b>then </b>
(  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp;  <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="pasch.html#E2:16"><i><font color="Green">E5</font></i></a>, <a class="txt" href="pasch.html#E2:16_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pasch.html#E4:16_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="pasch.html#E9:16_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="diraf.html#T36">DIRAF:36</a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><a NAME="E14:16_2"/><b>then </b>
 <a href="diraf.html#R3">LIN</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E1:16_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="pasch.html#E11:16_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/><b>hence </b><a NAME="E15:16_2"/>
contradiction
 <b>by </b><i><a class="txt" href="pasch.html#E1:16"><i><font color="Green">E4</font></i></a>, <a class="txt" href="pasch.html#E2:16_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pasch.html#E4:16_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="pasch.html#E6:16_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="diraf.html#T38">DIRAF:38</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:16"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="pasch.html#E9:16"><i><font color="Green">E12</font></i></a></i>;<br/>


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