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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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>













<b>assume </b><a NAME="E1:60"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a'</font>,<font color="Maroon">b'</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">K</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">a'</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">b</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/>

<b>set </b><font color="Maroon">A</font> =  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>;<br/>
<a NAME="E2:60"/><i><font color="Green">E39</font></i>: 
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:60"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> )
 
<b>by </b><i>, </i>;<br/>
<b>assume </b><a NAME="E4:60"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">a'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font>
 ;<br/>

<a NAME="E5:60"/><b>then </b>
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E6:60"><i><font color="Green">E52</font></i></a>, , <a class="ref" href="aff_1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E6:60"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="aff_1.html#R4" target="_self">//</a> <font color="Maroon">K</font>
 
<b>by </b><i>, , <a class="txt" href="aff_1.html#E15"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<a NAME="E7:60"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:60"/><b>then </b>
 <a href="aff_1.html#K2" target="_self">Line</a> <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font>
 
<b>by </b><i>, , <a class="txt" href="aff_1.html#E4:60"><i><font color="Green">E50</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:60"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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