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<b>let </b><font color="Maroon">SAS</font> be   <a href="semi_af1.html#NM1">Semi_Affine_Space</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/>





<b>consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E2:80"/><i><font color="Green">E29</font></i>: 
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E3:80"/>
(  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">a</font>,<font color="Maroon">x</font>,<font color="Maroon">o</font> &amp;  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font>,<font color="Maroon">o</font> )
 
<b>by </b><i><a class="ref" href="semi_af1.html#T43" target="_self">Th43</a>, <a class="ref" href="semi_af1.html#T40" target="_self">Th40</a>, <a class="ref" href="semi_af1.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E4:80"/><b>then </b>
 <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">a</font>,<font color="Maroon">x</font>,<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="semi_af1.html#T25" target="_self">Th25</a></i>;<br/>
<b>hence </b><a NAME="E5:80"/>
 ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font> st  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">a</font>,<font color="Olive">x</font>,<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>


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