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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">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>;<br/><b>let </b><font color="Maroon">s</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>assume </b><a NAME="E1:90"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:90_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s</font> )
 ;<br/><b>consider </b><font color="Maroon">t</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font><b> such that </b><br/><a NAME="E3:90_1"/><i><font color="Green">E31</font></i>: 
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T26" target="_self">Th26</a></i>;<br/><a NAME="E4:90_1"/>
(  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<font color="Maroon">t</font> &amp;  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">q</font>,<font color="Maroon">s</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T55" target="_self">Th55</a>, <a class="ref" href="semi_af1.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E5:90_1"/><b>then </b>
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">r</font>,<font color="Maroon">t</font>,<font color="Maroon">s</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T29" target="_self">Th29</a></i>;<br/><a NAME="E6:90_1"/><b>then </b>
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>,<font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E7:90_1"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> &amp; <font color="Maroon">r</font>,<font color="Maroon">s</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T54" target="_self">Th54</a>, <a class="ref" href="semi_af1.html#T13" target="_self">Th13</a>, <a class="ref" href="semi_af1.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E8:90_1"/><b>then </b><i><font color="Green">E32</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#D3" target="_self">Def3</a>, <a class="ref" href="semi_af1.html#T54" target="_self">Th54</a>, <a class="ref" href="semi_af1.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E9:90_1"/>
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">p</font>,<font color="Maroon">r</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T40" target="_self">Th40</a></i>;<br/><a NAME="E10:90_1"/><b>then </b>
(  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">p</font>,<font color="Maroon">o</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>,<font color="Maroon">r</font> &amp;  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">o</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="semi_af1.html#T55" target="_self">Th55</a>, <a class="ref" href="semi_af1.html#T33" target="_self">Th33</a></i>;<br/><a NAME="E11:90_1"/><b>then </b>
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>,<font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E12:90_1"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>,<font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E13:90_1"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>
 <b>by </b><i/>;<br/><a NAME="E14:90_1"/><b>then </b>
<font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T54" target="_self">Th54</a>, <a class="ref" href="semi_af1.html#T56" target="_self">Th56</a>, </i>;<br/><a NAME="E15:90_1"/><b>then </b>
<font color="Maroon">t</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E16:90_1"/>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T56" target="_self">Th56</a>, <a class="ref" href="semi_af1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:90"/>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a>  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>,<font color="Maroon">o</font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">q</font>,<font color="Maroon">s</font>,<font color="Maroon">o</font>
 <b>by </b><i>, <a class="ref" href="semi_af1.html#T51" target="_self">Th51</a></i>;<br/>


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