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<b>let </b><font color="Maroon">UN</font> be   <a href="classes2.html#NM1">Universe</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="grcat_1.html#K19" target="_self">GroupObjects</a> <font color="Maroon">UN</font>;<br/>



<b>consider </b><font color="Maroon">u</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:83"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">UN</font> &amp;  <a href="grcat_1.html#R1" target="_self">GO</a> <font color="Maroon">u</font>,<font color="Maroon">x</font> )
 <b>by </b><i/>;<br/>
<a NAME="E3:83"/>
 ex <font color="Olive">x1</font>, <font color="Olive">x2</font>, <font color="Olive">x3</font>, <font color="Olive">x4</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">x1</font>,<font color="Olive">x2</font>,<font color="Olive">x3</font>,<font color="Olive">x4</font></span><a href="mcart_1.html#K4">]</a></span> &amp;  ex <font color="Olive">G</font> being <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">G</font> &amp; <font color="Olive">x1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">G</font> &amp; <font color="Olive">x2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Olive">G</font> &amp; <font color="Olive">x3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Olive">G</font> &amp; <font color="Olive">x4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Olive">G</font> ) )
 
<b>by </b><i><a class="ref" href="grcat_1.html#T5" target="_self">Th5</a>, </i>;<br/>
<b>hence </b><a NAME="E4:83"/>
<font color="Maroon">x</font> is  <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a>
 ;<br/>


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