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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>assume </b><a NAME="E1:71"/><i><font color="Green">E58</font></i>: 
 <a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="incproj.html#NM2">IncProjSp</a>
 ;<br/>

<b>assume </b><a NAME="E2:71"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is   <a href="diraf.html#NM2">AffinPlane</a>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="afproj.html#K14" target="_self">ProjHorizon</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span>, <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:71"/><i><font color="Green">E60</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="afproj.html#E1:71"><i><font color="Green">E58</font></i></a>, <a class="ref" href="incproj.html#D11">INCPROJ:def 11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:71"/><i><font color="Green">E61</font></i>: 
( <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>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i><a class="ref" href="afproj.html#T21" target="_self">Th21</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:71"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="afproj.html#K6" target="_self">PDir</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="aff_4.html#NR1" target="_self">is_plane</a>  )
 <b>by </b><i><a class="ref" href="afproj.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E9:71"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="afproj.html#E2:71"><i><font color="Green">E59</font></i></a>, <a class="txt" href="afproj.html#E8:71"><i><font color="Green">E62</font></i></a>, <a class="ref" href="afproj.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E10:71"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="aff_4.html#R1">'||'</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="afproj.html#E6:71"><i><font color="Green">E61</font></i></a>, <a class="txt" href="afproj.html#E8:71"><i><font color="Green">E62</font></i></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="txt" href="afproj.html#E4:71"><i><font color="Green">E60</font></i></a>, <a class="txt" href="afproj.html#E6:71"><i><font color="Green">E61</font></i></a>, <a class="txt" href="afproj.html#E8:71"><i><font color="Green">E62</font></i></a>, <a class="ref" href="afproj.html#T36" target="_self">Th36</a></i>;<br/>


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