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<b>let </b><font color="Maroon">AFS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM2">Permutation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">AFS</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AFS</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AFS</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:121"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">f</font> <a href="transgeo.html#NR10" target="_self">is_Col</a> 
 <b>and </b><br/><a NAME="E2:121"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 ;<br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font>, <font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AFS</font><b> such that </b><br/><a NAME="E4:121"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="transgeo.html#D8" target="_self">Def8</a>, <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/>
<a NAME="E5:121"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="transgeo.html#T44" target="_self">Th44</a>, <a class="ref" href="transgeo.html#T51" target="_self">Th51</a>, <a class="ref" href="transgeo.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E6:121"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font> )
 
<b>by </b><i><a class="ref" href="transgeo.html#T51" target="_self">Th51</a>, <a class="ref" href="funct_2.html#T85">FUNCT_2:85</a></i>;<br/>
<a NAME="E7:121"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#T44" target="_self">Th44</a>, <a class="ref" href="transgeo.html#T51" target="_self">Th51</a>, </i>;<br/>
<b>hence </b><a NAME="E8:121"/>
<font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="transgeo.html#T56" target="_self">Th56</a>, <a class="ref" href="aff_1.html#T51">AFF_1:51</a></i>;<br/>


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