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





<b>assume </b><a NAME="E1:6"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">h</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 ;<br/>

<a NAME="E2:6"/>
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> <a href="group_2.html#K13">*</a> <font color="Maroon">h</font> holds <br/><font color="Olive">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> <a href="group_2.html#K13">*</a> <font color="Maroon">h</font>
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:6_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h</font> &amp; <font color="Maroon">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> )
 <b>by </b><i><a class="ref" href="group_2.html#T126">GROUP_2:126</a></i>;<br/>
<a NAME="E4:6_1"/>
<font color="Maroon">g</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i>, , <a class="ref" href="group_2.html#T59">GROUP_2:59</a></i>;<br/>
<b>hence </b><a NAME="E5:6_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>
 <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="E3:6"/>
<font color="Maroon">H</font> <a href="group_2.html#K13">*</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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