<?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">H1</font>, <font color="Maroon" title="c3">H2</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>thus </b><a NAME="E1:107"/>
( <font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  implies  ex <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c3">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Olive" title="b1">g</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><a NAME="E1:107_1"/><i><font color="Green" title="E76">A1</font></i>: 
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H1</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">H1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c4">g</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D11" target="_self" title="GROUP_3:def.11">GROUP_3:def 11</a><br/>

<a NAME="E2:107_1"/>
<font color="Maroon" title="c2">H1</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">H2</font>
 
<b>by </b><i><a class="txt" href="group_3.html#E1:107_1"><i><font color="Green" title="E76">A1</font></i></a>, <a class="ref" href="group_3.html#T74" target="_self" title="GROUP_3:th.74">Th74</a></i>;<br/>
<b>hence </b><a NAME="E3:107_1"/>
 ex <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c3">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Olive" title="b1">g</font>
 ;<br/>


</div><b>end;</b></div>

<b>given </b><font color="Maroon" title="c4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><a NAME="E2:107"/><i><font color="Green" title="E76">A2</font></i>: 
<font color="Maroon" title="c3">H2</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c4">g</font>
 ;<br/>

<a NAME="E3:107"/>
<font color="Maroon" title="c2">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="group_3.html#E2:107"><i><font color="Green" title="E76">A2</font></i></a>, <a class="ref" href="group_3.html#T74" target="_self" title="GROUP_3:th.74">Th74</a></i>;<br/>
<b>hence </b><a NAME="E4:107"/>
<font color="Maroon" title="c2">H1</font>,<font color="Maroon" title="c3">H2</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#D11" target="_self" title="GROUP_3:def.11">Def11</a></i>;<br/>


</div>
