<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">N1</font> be  <a href="group_1.html#V1">strict</a> <a href="group_3.html#V1" target="_self">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>, <font color="Maroon">N2</font> be  <a href="group_1.html#V1">strict</a> <a href="group_3.html#V1" target="_self">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>set </b><font color="Maroon">A</font> = <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">B</font> =  <a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font>;<br/>
<b>set </b><font color="Maroon">C</font> =  <a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font>;<br/>
<a NAME="E1:136"/>
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_3.html#T59" target="_self">Th59</a></i>;<br/>
<b>then consider </b><font color="Maroon">H</font> being  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:136"/><i><font color="Green">E38</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T93">GROUP_2:93</a></i>;<br/>
<a NAME="E4:136"/><i><font color="Green">E39</font></i>: 
 <a href="group_2.html#K7">carr</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_3.html#T61" target="_self">Th61</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="136_1"><b>now </b></a><div class="add"><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>thus </b><font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">H</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>
<b>by </b><i><a class="ref" href="group_3.html#T63" target="_self">Th63</a>, <a class="ref" href="group_2.html#T35">GROUP_2:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">N1</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>
<b>by </b><i><a class="ref" href="group_3.html#T51" target="_self">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N2</font></span>)</span>
<b>by </b><i><a class="ref" href="group_2.html#T36">GROUP_2:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">N2</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_3.html#T51" target="_self">Th51</a></i>
<br/>.= 
<font color="Maroon">H</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="group_2.html#T37">GROUP_2:37</a>, <a class="ref" href="group_3.html#T63" target="_self">Th63</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E6:136"/><b>then </b>
<font color="Maroon">H</font> is  <a href="group_3.html#V1" target="_self">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T51" target="_self">Th51</a></i>;<br/>
<b>hence </b><a NAME="E7:136"/>
 ex <font color="Olive">N</font> being <a href="group_1.html#V1">strict</a> <a href="group_3.html#V1" target="_self">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N1</font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">N2</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_3.html#T61" target="_self">Th61</a></i>;<br/>


</div>
