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

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">N1</font>, <font color="Maroon" title="c3">N2</font> be  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a> <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>set </b><font color="Maroon" title="c4">A</font> = <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">B</font> =  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">C</font> =  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font>;<br/>
<a NAME="E1:135"/>
<span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_3.html#T148" target="_self" title="GROUP_3:th.148">Th148</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">H</font> being  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:135"/><i><font color="Green" title="E87">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T93" title="GROUP_2:th.93">GROUP_2:93</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>thus </b><font color="Maroon" title="c8">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c7">H</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span>
<b>by </b><i><a class="txt" href="group_3.html#E3:135"><i><font color="Green" title="E87">A1</font></i></a>, <a class="ref" href="group_2.html#T35" title="GROUP_2:th.35">GROUP_2:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">N1</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span>
<b>by </b><i><a class="ref" href="group_3.html#T140" target="_self" title="GROUP_3:th.140">Th140</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">N2</font></span>)</span>
<b>by </b><i><a class="ref" href="group_2.html#T36" title="GROUP_2:th.36">GROUP_2:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">N2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c8">a</font></span>)</span>
<b>by </b><i><a class="ref" href="group_3.html#T140" target="_self" title="GROUP_3:th.140">Th140</a></i>
<br/>.= 
<font color="Maroon" title="c7">H</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c8">a</font>
<b>by </b><i><a class="txt" href="group_3.html#E3:135"><i><font color="Green" title="E87">A1</font></i></a>, <a class="ref" href="group_2.html#T37" title="GROUP_2:th.37">GROUP_2:37</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:135"/><b>then </b>
<font color="Maroon" title="c7">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_3.html#T140" target="_self" title="GROUP_3:th.140">Th140</a></i>;<br/>
<b>hence </b><a NAME="E6:135"/>
 ex <font color="Olive" title="b1">N</font> being <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a> <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">N1</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">N2</font></span>)</span>
 <b>by </b><i><a class="txt" href="group_3.html#E3:135"><i><font color="Green" title="E87">A1</font></i></a></i>;<br/>


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