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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="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">y</font> be    <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>;<br/><b>let </b><font color="Maroon">X</font> be    <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#K13" target="_self">IncProjSp_of</a> <font color="Maroon">AS</font></span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green">E26</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">X</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U3">Inc</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> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">X</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U3">Inc</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>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font>, <font color="Maroon">b</font> = <font color="Maroon">y</font> as   <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> <b>by </b><i/>;<br/>
<a NAME="E4:56"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, <a class="ref" href="incsp_1.html#D1">INCSP_1:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">X1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E6:56"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">X1</font> &amp; <font color="Maroon">X1</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">X2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E8:56"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K5" target="_self">LDir</a> <font color="Maroon">X2</font> &amp; <font color="Maroon">X2</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="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="E10:56"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">x</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">y</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Y</font> )
 <b>by </b><i><a class="ref" href="afproj.html#T2" target="_self">Th2</a></i>;<br/>
<b>take </b>
<font color="Maroon">Y</font>
;<br/>

<b>consider </b><font color="Maroon">Z</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E12:56"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K6" target="_self">PDir</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">Z</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/>
<b>reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">Y</font>,2</span><a href="tarski.html#K4">]</a></span> as   <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> <b>by </b><i><a class="txt" href="afproj.html#E1:56"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E14:56"/>
( <font color="Maroon">X1</font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">X2</font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">Z</font> )
 
<b>by </b><i>, , , , <a class="txt" href="afproj.html#E12:56"><i><font color="Green">E35</font></i></a></i>;<br/>
<a NAME="E15:56"/><b>then </b>
( <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E16:56"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">Y</font>,2</span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i>, , <a class="ref" href="afproj.html#T5" target="_self">Th5</a></i>;<br/>


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