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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">p</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">AS</font></span>)</span>;<br/><b>let </b><font color="Maroon">A</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">AS</font></span>)</span>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">X</font>,1</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">X</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> )
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">p</font> is  not   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>
 ;<br/>

<b>consider </b><font color="Maroon">Xp</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E4:43"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">Xp</font> &amp; <font color="Maroon">Xp</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i>, </i>;<br/>
<a NAME="E5:43"/>
<font color="Maroon">Xp</font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">X</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:43"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">X</font>
 <b>by </b><i>, , </i>;<br/>


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