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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:44"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,1</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>and </b><br/><a NAME="E2:44"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E3:44"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is  not   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E4:44"/>
<font color="Maroon">c<sub>4</sub></font> is  not   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E5:44"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="afproj.html#E1:44"><i><font color="Green">E37</font></i></a>, <a class="txt" href="afproj.html#E2:44"><i><font color="Green">E38</font></i></a>, <a class="txt" href="afproj.html#E3:44"><i><font color="Green">E39</font></i></a>, <a class="ref" href="afproj.html#T34" target="_self">Th34</a></i>;<br/>
<b>hence </b><a NAME="E6:44"/>
contradiction
 <b>by </b><i><a class="txt" href="afproj.html#E2:44"><i><font color="Green">E38</font></i></a></i>;<br/>


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