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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_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">H</font> is <a href="group_3.html#V1">normal</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">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E2:2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>
 ;<br/>

<b>set </b><font color="Maroon">A</font> =  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font>;<br/>
<b>consider </b><font color="Maroon">q</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>
<a NAME="E5:2"/>
<font color="Maroon">q</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E6:2"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font> &amp; <font color="Maroon">b</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> )
 
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E7:2"/>
<font color="Maroon">H</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="group_3.html#T140">GROUP_3:140</a></i>;<br/>
<a NAME="E8:2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_2.html#T128">GROUP_2:128</a></i>;<br/>
<a NAME="E9:2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T127">GROUP_2:127</a></i>;<br/>
<a NAME="E10:2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>;<br/>
<a NAME="E11:2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T132">GROUP_2:132</a></i>;<br/>
<a NAME="E12:2"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="group_3.html#K6">|^</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T71">GROUP_3:71</a></i>;<br/>
<a NAME="E13:2"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span> <a href="group_3.html#K4">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_3.html#D6">GROUP_3:def 6</a></i>;<br/>
<a NAME="E14:2"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K3">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="group_2.html#T33">GROUP_2:33</a></i>;<br/>
<a NAME="E15:2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K3">*</a> <span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T34">GROUP_2:34</a></i>;<br/>
<a NAME="E16:2"/><b>then </b>
<font color="Maroon">b</font> <a href="group_3.html#K2">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_2.html#K3">*</a> <span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">a</font>
 
;<br/>
<a NAME="E17:2"/><b>then </b>
<font color="Maroon">b</font> <a href="group_3.html#K2">|^</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="group_3.html#T59">GROUP_3:59</a></i>;<br/>
<b>hence </b><a NAME="E18:2"/>
<font color="Maroon">b</font> <a href="group_3.html#K2">|^</a> <font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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