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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">H1</font> be    <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="c4">X</font>, <font color="Maroon" title="c5">Y</font> be    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H1</font>;<br/><b>let </b><font color="Maroon" title="c6">X'</font>, <font color="Maroon" title="c7">Y'</font> be    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>;<br/>









<b>assume </b><a NAME="E1:116"/>
( <font color="Maroon" title="c4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">X'</font> &amp; <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y'</font> )
 ;<br/>

<a NAME="E2:116"/><b>then </b><i><font color="Green" title="E92">A1</font></i>: 
( 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="c4">X</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">X</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">Y</font></span>)</span> &amp; 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="c6">X'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c7">Y'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c6">X'</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c7">Y'</font></span>)</span> &amp;  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">X</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 <font color="Maroon" title="c4">X</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">Y</font> &amp;  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c6">X'</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 <font color="Maroon" title="c4">X</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c7">Y'</font> )
 
<b>by </b><i><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">Z</font> = <font color="Maroon" title="c4">X</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">Y</font> as    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> <b>by </b><i><a class="ref" href="group_9.html#T11" target="_self" title="GROUP_9:th.11">Th11</a></i>;<br/>
<a NAME="E4:116"/>
<font color="Maroon" title="c6">X'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c7">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Z</font>
 
<b>by </b><i><a class="txt" href="group_9.html#E2:116"><i><font color="Green" title="E92">A1</font></i></a>, <a class="ref" href="group_9.html#T18" target="_self" title="GROUP_9:th.18">Th18</a></i>;<br/>
<b>hence </b><a NAME="E5:116"/>
<font color="Maroon" title="c6">X'</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c7">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">Y</font>
 ;<br/>


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