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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">a</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" title="AFPROJ:func.13">IncProjSp_of</a> <font color="Maroon" title="c1">AS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">A</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="afproj.html#K13" title="AFPROJ:func.13">IncProjSp_of</a> <font color="Maroon" title="c1">AS</font></span>)</span>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">X</font>,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c2">X</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green" title="E33">A2</font></i>: 
( <font color="Maroon" title="c3">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c4">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p</font> )
 <b>and </b><br/><a NAME="E3:43"/><i><font color="Green" title="E34">A3</font></i>: 
<font color="Maroon" title="c3">p</font> is  not   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>
 ;<br/>

<b>assume </b><a NAME="E4:43"/>
<font color="Maroon" title="c4">a</font> is  not   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>
 ;<br/>

<a NAME="E5:43"/><b>then </b>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afproj.html#K5" title="AFPROJ:func.5">LDir</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afproj.html#K5" title="AFPROJ:func.5">LDir</a> <font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="txt" href="afproj.html#E1:43"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="afproj.html#E2:43"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="afproj.html#E3:43"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="afproj.html#T34" target="_self" title="AFPROJ:th.34">Th34</a></i>;<br/>
<b>hence </b><a NAME="E6:43"/>
contradiction
 <b>by </b><i><a class="txt" href="afproj.html#E2:43"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/>


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