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<b>let </b><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>;<br/><b>let </b><font color="Maroon" title="c3">H</font>, <font color="Maroon" title="c4">K</font>, <font color="Maroon" title="c5">H'</font>, <font color="Maroon" title="c6">K'</font> be  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>;<br/><b>let </b><font color="Maroon" title="c7">JH</font> be  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c5">H'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c8">JK</font> be  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c6">K'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:157"/><i><font color="Green" title="E132">A1</font></i>: 
( <font color="Maroon" title="c7">JH</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c6">K'</font></span>)</span> &amp; <font color="Maroon" title="c8">JK</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">K'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H'</font></span>)</span> )
 ;<br/>

<b>assume </b><a NAME="E2:157"/><i><font color="Green" title="E133">A2</font></i>: 
<font color="Maroon" title="c5">H'</font> is  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font>
 ;<br/>

<b>assume </b><a NAME="E3:157"/><i><font color="Green" title="E134">A3</font></i>: 
<font color="Maroon" title="c6">K'</font> is  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">K</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c9">HK</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">H'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span>;<br/>
<a NAME="E4:157"/>
( <font color="Maroon" title="c5">H'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font> is  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font> &amp; <font color="Maroon" title="c6">K'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font> is  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font> )
 
<b>by </b><i><a class="txt" href="group_9.html#E3:157"><i><font color="Green" title="E134">A3</font></i></a>, <a class="txt" href="group_9.html#E2:157"><i><font color="Green" title="E133">A2</font></i></a>, <a class="ref" href="group_9.html#T60" target="_self" title="GROUP_9:th.60">Th60</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">HK</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">H'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span> as  <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font> <b>by </b><i><a class="ref" href="group_9.html#T87" target="_self" title="GROUP_9:th.87">Th87</a></i>;<br/>
<a NAME="E6:157"/><i><font color="Green" title="E135">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">H'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c7">JH</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c10">HK</font> <a href="group_9.html#R3" title="GROUP_9:pred.3">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="group_9.html#T91" target="_self" title="GROUP_9:th.91">Th91</a>, <a class="txt" href="group_9.html#E1:157"><i><font color="Green" title="E132">A1</font></i></a>, <a class="txt" href="group_9.html#E2:157"><i><font color="Green" title="E133">A2</font></i></a>, <a class="txt" href="group_9.html#E3:157"><i><font color="Green" title="E134">A3</font></i></a></i>;<br/>
<a NAME="E7:157"/>
<font color="Maroon" title="c10">HK</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">H'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span>
 
;<br/>
<a NAME="E8:157"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">K'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c8">JK</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c10">HK</font> <a href="group_9.html#R3" title="GROUP_9:pred.3">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="group_9.html#T91" target="_self" title="GROUP_9:th.91">Th91</a>, <a class="txt" href="group_9.html#E1:157"><i><font color="Green" title="E132">A1</font></i></a>, <a class="txt" href="group_9.html#E2:157"><i><font color="Green" title="E133">A2</font></i></a>, <a class="txt" href="group_9.html#E3:157"><i><font color="Green" title="E134">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:157"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">H'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">K</font></span>)</span></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c7">JH</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">K'</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">K</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span></span>)</span> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c8">JK</font> <a href="group_9.html#R3" title="GROUP_9:pred.3">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="group_9.html#E6:157"><i><font color="Green" title="E135">A4</font></i></a>, <a class="ref" href="group_9.html#T55" target="_self" title="GROUP_9:th.55">Th55</a></i>;<br/>


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