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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">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:48"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">M</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 <b>and </b><br/><a NAME="E2:48"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">X</font> <a href="aff_4.html#NR1" target="_self">is_plane</a> 
 ;<br/>

<b>assume </b><a NAME="E3:48"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  holds <br/>(  not <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> or <font color="Olive">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E5:48"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>and </b><br/><a NAME="E6:48"/><i><font color="Green">E43</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E9"><i><font color="Green">Lemma42</font></i></a>, <a class="ref" href="aff_4.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E7:48"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E6:48"><i><font color="Green">E43</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E8:48"/>
contradiction
 <b>by </b><i><a class="ref" href="aff_4.html#T7" target="_self">Th7</a>, , <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/>


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