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<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">H2</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">H1</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="E1:120"/>
( <font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">H2</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  implies  <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H1</font>, <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">H2</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c4">a</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="E1:120_1"/><i><font color="Green" title="E85">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="c3">H1</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c3">H1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c4">a</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="E2:120_1"/>
 <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H1</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">H2</font></span>)</span> <a href="group_3.html#K4" title="GROUP_3:func.4">|^</a> <font color="Maroon" title="c4">a</font>
 
<b>by </b><i><a class="txt" href="group_3.html#E1:120_1"><i><font color="Green" title="E85">A1</font></i></a>, <a class="ref" href="group_3.html#D6" target="_self" title="GROUP_3:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E3:120_1"/>
 <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H1</font>, <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c2">H2</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#D9" target="_self" title="GROUP_3:def.9">Def9</a></i>;<br/>


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

<b>given </b><font color="Maroon" title="c4">a</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="E2:120"/><i><font color="Green" title="E85">A2</font></i>: 
 <a href="group_2.html#K7" title="GROUP_2:func.7">carr</a> <font color="Maroon" title="c3">H1</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">H2</font></span>)</span> <a href="group_3.html#K4" title="GROUP_3:func.4">|^</a> <font color="Maroon" title="c4">a</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D9" target="_self" title="GROUP_3:def.9">GROUP_3:def 9</a><br/>

<a NAME="E3:120"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c4">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="group_3.html#E2:120"><i><font color="Green" title="E85">A2</font></i></a>, <a class="ref" href="group_3.html#D6" target="_self" title="GROUP_3:def.6">Def6</a></i>;<br/>
<a NAME="E4:120"/><b>then </b>
<font color="Maroon" title="c3">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c4">a</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T68" title="GROUP_2:th.68">GROUP_2:68</a></i>;<br/>
<b>hence </b><a NAME="E5:120"/>
<font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">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/>


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