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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">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font>, <font color="Maroon" title="c4">N</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>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font> )
 <b>and </b><br/><a NAME="E2:51"/><i><font color="Green" title="E45">A2</font></i>: 
( <font color="Maroon" title="c3">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c4">N</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E4:51"/><i><font color="Green" title="E46">A3</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">q</font>
 <b>and </b><br/><a NAME="E5:51"/><i><font color="Green" title="E47">A4</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:51"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/>
<a NAME="E6:51"/><i><font color="Green" title="E48">A5</font></i>: 
<font color="Maroon" title="c4">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:51"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:51"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="aff_4.html#E4:51"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="aff_4.html#E5:51"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E8:51"/><i><font color="Green" title="E49">A6</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X</font> &amp; <font color="Maroon" title="c3">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">X</font> &amp; <font color="Maroon" title="c6">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  )
 <b>by </b><i><a class="txt" href="aff_4.html#E2:51"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="aff_4.html#T36" target="_self" title="AFF_4:th.36">Th36</a></i>;<br/>
<a NAME="E9:51"/>
<font color="Maroon" title="c4">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">X</font>
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:51"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:51"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="aff_4.html#E6:51"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="aff_4.html#E8:51"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="aff_4.html#T19" target="_self" title="AFF_4:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E10:51"/>
 ex <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Maroon" title="c3">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Maroon" title="c4">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b1">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  )
 <b>by </b><i><a class="txt" href="aff_4.html#E8:51"><i><font color="Green" title="E49">A6</font></i></a></i>;<br/>


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