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<b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="collsp.html#V4" target="_self">proper</a> <a href="collsp.html#NM2">CollSp</a>;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="collsp.html#M2" target="_self">LINE</a> of <font color="Maroon">c<sub>10</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font><b> such that </b><br/><a NAME="E5:36"/>
<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>
 <b>and </b><br/><a NAME="E6:36"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="collsp.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="collsp.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E7:36"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="collsp.html#E2:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="collsp.html#E3:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="collsp.html#E6:36"><i><font color="Green">E32</font></i></a>, <a class="ref" href="collsp.html#T17" target="_self">Th17</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E8:36"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="collsp.html#K1" target="_self">Line</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>10</sub></font><b> such that </b><br/><a NAME="E10:36"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>and </b><br/><a NAME="E11:36"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 ;<br/>
<a NAME="E12:36"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="collsp.html#R1" target="_self">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="collsp.html#E1:36"><i><font color="Green">E29</font></i></a>, <a class="txt" href="collsp.html#E7:36"><i><font color="Green">E33</font></i></a>, <a class="txt" href="collsp.html#E11:36"><i><font color="Green">E35</font></i></a>, <a class="ref" href="collsp.html#T14" target="_self">Th14</a></i>;<br/>
<b>hence </b><a NAME="E13:36"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="collsp.html#E6:36"><i><font color="Green">E32</font></i></a>, <a class="txt" href="collsp.html#E10:36"><i><font color="Green">E34</font></i></a></i>;<br/>


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