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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="anproj_2.html#V7">up-3-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</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>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</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="E1:29"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</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>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</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> <a href="projdes1.html#R2" target="_self">constitute_a_quadrangle</a> 
 <b>and </b><br/><a NAME="E3:29"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<a NAME="E4:29"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</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>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E2:29"><i><font color="Green">E26</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projdes1.html#D2" target="_self">Def2</a></i>;<br/>
<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_1"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 ;<br/><a NAME="E2:29_1"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projdes1.html#T23" target="_self">Th23</a></i>;<br/><b>hence </b><a NAME="E3:29_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E1:29_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="projdes1.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 ;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:29_2"/><i><font color="Green">E31</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E4:29"><i><font color="Green">E28</font></i></a>, <a class="ref" href="projdes1.html#T17" target="_self">Th17</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:29_2"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>12</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>2</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D10">ANPROJ_2:def 10</a></i>;<br/><a NAME="E6:29_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:29_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="anproj_2.html#D9">ANPROJ_2:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>15</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:29_2"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E6:29_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="anproj_2.html#D9">ANPROJ_2:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>16</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="E12:29_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E6:29_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="anproj_2.html#D9">ANPROJ_2:def 9</a></i>;<br/><a NAME="E13:29_2"/><i><font color="Green">E37</font></i>: 
( not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E4:29"><i><font color="Green">E28</font></i></a>, <a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E14:29_2"/><b>then </b><i><font color="Green">E38</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="projdes1.html#E3:29_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projdes1.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E15:29_2"/>
( not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="projdes1.html#E3:29_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projdes1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E16:29_2"/><b>then </b><i><font color="Green">E39</font></i>: 
not <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E13:29_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="projdes1.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E17:29_2"/>
( not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="projdes1.html#E3:29_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projdes1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E18:29_2"/><b>then </b><i><font color="Green">E40</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E13:29_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="projdes1.html#T22" target="_self">Th22</a></i>;<br/><a NAME="E19:29_2"/><b>then </b><i><font color="Green">E41</font></i>: 
not <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E1:29_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="projdes1.html#E3:29_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E8:29_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="projdes1.html#E10:29_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="projdes1.html#E12:29_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="projdes1.html#E14:29_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="projdes1.html#E16:29_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="projdes1.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E20:29_2"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E14:29_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="projdes1.html#T23" target="_self">Th23</a></i>;<br/><a NAME="E21:29_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E8:29_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="projdes1.html#E10:29_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="projdes1.html#E14:29_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="projdes1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E22:29_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E23:29_2"/>
not <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E16:29_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="projdes1.html#T23" target="_self">Th23</a></i>;<br/><a NAME="E24:29_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E10:29_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="projdes1.html#E12:29_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="projdes1.html#E16:29_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="projdes1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E25:29_2"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E26:29_2"/>
not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E18:29_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="projdes1.html#T23" target="_self">Th23</a></i>;<br/><a NAME="E27:29_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E8:29_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="projdes1.html#E12:29_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="projdes1.html#E18:29_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="projdes1.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E28:29_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E29:29_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E8:29_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E30:29_2"/>
not <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E14:29_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="projdes1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E31:29_2"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E32:29_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="projdes1.html#E1:29"><i><font color="Green">E25</font></i></a>, <a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E5:29_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projdes1.html#E29:29_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="projdes1.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E33:29_2"/><b>then </b><i><font color="Green">E46</font></i>: 
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E3:29_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="projdes1.html#E29:29_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="projdes1.html#T19" target="_self">Th19</a></i>;<br/><a NAME="E34:29_2"/><i><font color="Green">E47</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> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>14</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>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>by </b><i><a class="txt" href="projdes1.html#E4:29"><i><font color="Green">E28</font></i></a>, <a class="txt" href="projdes1.html#E19:29_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/><a NAME="E35:29_2"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i><a class="ref" href="projdes1.html#T18" target="_self">Th18</a></i>;<br/><a NAME="E36:29_2"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E3:29"><i><font color="Green">E27</font></i></a>, <a class="txt" href="projdes1.html#E34:29_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="projdes1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E37:29_2"/>
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a>  )
 <b>by </b><i><a class="txt" href="projdes1.html#E22:29_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="projdes1.html#E25:29_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="projdes1.html#E28:29_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="projdes1.html#E34:29_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="projdes1.html#E35:29_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="projdes1.html#T14" target="_self">Th14</a></i>;<br/><b>hence </b><a NAME="E38:29_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E4:29"><i><font color="Green">E28</font></i></a>, <a class="txt" href="projdes1.html#E19:29_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="projdes1.html#E33:29_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="projdes1.html#E36:29_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="projdes1.html#T20" target="_self">Th20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:29"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E5:29"><i><font color="Green">E29</font></i></a></i>;<br/>


</div>
