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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>thus </b><a NAME="E1:41"/>
( <font color="Maroon" title="c2">h</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font> implies <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:41_1"/>
<font color="Maroon" title="c2">h</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<a NAME="E2:41_1"/><b>then </b>
<font color="Maroon" title="c2">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_1.html#T45" target="_self" title="GROUP_1:th.45">Th45</a></i>;<br/>
<b>hence </b><a NAME="E3:41_1"/>
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 <b>by </b><i><a class="ref" href="group_1.html#T20" target="_self" title="GROUP_1:th.20">Th20</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:41"/>
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 ;<br/>

<b>hence </b><font color="Maroon" title="c2">h</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> 2 = 
<font color="Maroon" title="c2">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T45" target="_self" title="GROUP_1:th.45">Th45</a></i>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="ref" href="group_1.html#D6" target="_self" title="GROUP_1:def.6">Def6</a></i>
;<br/><br/>


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