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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="semi_af1.html#NM1">Semi_Affine_Space</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:80"/><i><font color="Green">E68</font></i>: 
 <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T82" target="_self">Th82</a></i>;<br/>
<a NAME="E3:80"/>
(  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>, <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="semi_af1.html#R3" target="_self">congr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="semi_af1.html#E2:80"><i><font color="Green">E68</font></i></a>, <a class="ref" href="semi_af1.html#D5" target="_self">Def5</a>, <a class="ref" href="semi_af1.html#T89" target="_self">Th89</a></i>;<br/>
<a NAME="E4:80"/><b>then </b>
 <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="semi_af1.html#T81" target="_self">Th81</a></i>;<br/>
<b>hence </b><a NAME="E5:80"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st  <a href="semi_af1.html#K1" target="_self">sum</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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