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<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="grcat_1.html#K19" title="GRCAT_1:func.19">GroupObjects</a> <font color="Maroon" title="c1">UN</font>;<br/>



<b>consider </b><font color="Maroon" title="c3">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:81"/><i><font color="Green" title="E46">A1</font></i>: 
( <font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">UN</font> &amp;  <a href="grcat_1.html#R1" title="GRCAT_1:pred.1">GO</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="ref" href="grcat_1.html#D29" target="_self" title="GRCAT_1:def.29">Def29</a></i>;<br/>
<a NAME="E3:81"/>
 ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> &amp;  ex <font color="Olive" title="b5">G</font> being <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a> st <br/>( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">G</font> &amp; <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b5">G</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Olive" title="b5">G</font> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Olive" title="b5">G</font> &amp; <font color="Olive" title="b4">x4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Olive" title="b5">G</font> ) )
 
<b>by </b><i><a class="txt" href="grcat_1.html#E2:81"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="grcat_1.html#D28" target="_self" title="GRCAT_1:def.28">Def28</a></i>;<br/>
<b>hence </b><a NAME="E4:81"/>
<font color="Maroon" title="c2">x</font> is  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a>
 ;<br/>


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