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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/>

<b>assume </b><a NAME="E1:71"/><i><font color="Green">E25</font></i>: 
 <a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">AS</font> is   <a href="incproj.html#NM2">IncProjSp</a>
 ;<br/>

<b>assume </b><a NAME="E2:71"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">AS</font> is   <a href="diraf.html#NM2">AffinPlane</a>
 ;<br/>

<b>set </b><font color="Maroon">XX</font> =  <a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">AS</font>;<br/>
<b>consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="incsp_1.html#U1">Points</a> of <span class="p1">(<span class="default"><a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">AS</font></span>)</span>, <font color="Maroon">A</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="incsp_1.html#U2">Lines</a> of <span class="p1">(<span class="default"><a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">AS</font></span>)</span><b> such that </b><br/><a NAME="E4:71"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="incproj.html#D11">INCPROJ:def 11</a></i>;<br/>
<b>consider </b><font color="Maroon">X</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E6:71"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">Y</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E8:71"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K6" target="_self">PDir</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="aff_4.html#NR1" target="_self">is_plane</a>  )
 <b>by </b><i><a class="ref" href="afproj.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E9:71"/>
<font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AS</font>
 
<b>by </b><i>, <a class="ref" href="afproj.html#D6" target="_self">Def6</a>, </i>;<br/>
<a NAME="E10:71"/><b>then </b>
<font color="Maroon">X</font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="afproj.html#D5" target="_self">Def5</a>, <a class="ref" href="afproj.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_4.html#T42">AFF_4:42</a></i>;<br/>
<b>hence </b><a NAME="E11:71"/>
contradiction
 <b>by </b><i>, <a class="ref" href="afproj.html#D5" target="_self">Def5</a>, <a class="ref" href="afproj.html#D6" target="_self">Def6</a>, </i>;<br/>


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