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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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:47"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">H</font> is <a href="group_4.html#V2" target="_self">maximal</a>
 <b>and </b><br/><a NAME="E2:47"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 ;<br/>

<a NAME="E3:47"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:47"/><b>then </b>
(  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:47"/><b>then </b>
(  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> is    <a href="group_2.html#M1">Subgroup</a> of  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:47"/><b>then </b>
( <font color="Maroon">H</font> is    <a href="group_2.html#M1">Subgroup</a> of  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> &amp; <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:47"/>
 <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">a</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="group_4.html#E1:47"><i><font color="Green">E31</font></i></a>, </i>;<br/>


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