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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><a NAME="E1:68"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">H</font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:68_1"/><i><font color="Green">E39</font></i>: 
not <font color="Maroon">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_1_1"/>
<font color="Maroon">g</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> <a href="group_3.html#K6" target="_self">|^</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E2:68_1_1"/><b>then </b>
 ex <font color="Olive">h</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <br/>( <font color="Maroon">g</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">h</font> <a href="group_3.html#K2" target="_self">|^</a> <font color="Maroon">a</font> &amp; <font color="Olive">h</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> )
 <b>by </b><i><a class="ref" href="group_3.html#T4" target="_self">Th4</a></i>;<br/><b>hence </b><a NAME="E3:68_1_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:68_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:68"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="group_2.html#T71">GROUP_2:71</a></i>;<br/>


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