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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font> being  <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/> for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font> being   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font> holds  <font color="Olive" title="b2">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b3">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">H1</font> <a href="group_9.html#K16" title="GROUP_9:func.16">*</a> <font color="Olive" title="b3">H2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> holds  <font color="Olive" title="b1">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Olive" title="b2">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">H1</font> <a href="group_9.html#K16" title="GROUP_9:func.16">*</a> <font color="Olive" title="b2">H2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font> be    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c4">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K16" title="GROUP_9:func.16">*</a> <font color="Maroon" title="c4">H2</font></span>)</span></span><br/>







<b>reconsider </b><font color="Maroon" title="c5">H1'</font> = <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c6">H2'</font> = <font color="Maroon" title="c4">H2</font> as    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G</font> <b>by </b><i><a class="ref" href="group_9.html#D7" target="_self" title="GROUP_9:def.7">Def7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">Y</font> = 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="c5">H1'</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c6">H2'</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">G</font> <b>by </b><i><a class="ref" href="group_2.html#D5" title="GROUP_2:def.5">GROUP_2:def 5</a></i>;<br/>
<a NAME="E3:105"/><i><font color="Green" title="E81">A1</font></i>: 
<font color="Maroon" title="c7">Y</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"><a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">H1'</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c6">H2'</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="group_4.html#T68" title="GROUP_4:th.68">GROUP_4:68</a></i>;<br/>
<font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c4">H2</font> = 
 <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <font color="Maroon" title="c7">Y</font>
<b>by </b><i><a class="txt" href="group_9.html#E89"><i><font color="Green" title="E78">Lm32</font></i></a></i>
<br/>.= 
 <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">H1'</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c6">H2'</font></span>)</span>
<b>by </b><i><a class="txt" href="group_9.html#E3:105"><i><font color="Green" title="E81">A1</font></i></a>, <a class="txt" href="group_9.html#E89"><i><font color="Green" title="E78">Lm32</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:105"/>
<font color="Maroon" title="c3">H1</font> <a href="group_9.html#K19" title="GROUP_9:func.19">"\/"</a> <font color="Maroon" title="c4">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_9.html#K18" title="GROUP_9:func.18">the_stable_subgroup_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="group_9.html#K16" title="GROUP_9:func.16">*</a> <font color="Maroon" title="c4">H2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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