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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>, <font color="Maroon" title="c4">H2</font>, <font color="Maroon" title="c5">H3</font> be    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>;<br/>









the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span></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">H3</font></span>)</span>
<b>by </b><i><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H2</font></span>)</span></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">H3</font></span>)</span>
<b>by </b><i><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">H1</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></i>
<br/>.= 
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="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_9.html#D28" target="_self" title="GROUP_9:def.28">Def28</a></i>
;<br/>
<b>hence </b><a NAME="E2:84"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">H3</font></span>)</span>
 <b>by </b><i><a class="txt" href="group_9.html#E12"><i><font color="Green" title="E12">Lm5</font></i></a></i>;<br/>


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