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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/>  for <font color="Olive" title="b2">H</font>, <font color="Olive" title="b3">F1</font>, <font color="Olive" title="b4">F2</font> being   <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="Olive" title="b1">G</font>  st <font color="Olive" title="b3">F1</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="Olive" title="b4">F2</font> holds <br/><font color="Olive" title="b2">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">F1</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="Olive" title="b2">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b4">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H</font>, <font color="Olive" title="b2">F1</font>, <font color="Olive" title="b3">F2</font> being   <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>  st <font color="Olive" title="b2">F1</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="Olive" title="b3">F2</font> holds <br/><font color="Olive" title="b1">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b2">F1</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="Olive" title="b1">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font>, <font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">F1</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="c5">F2</font> implies <font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">F1</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="c5">F2</font> )</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c6">F</font> = <font color="Maroon" title="c5">F2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font> as    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c5">F2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E101"><span class="lab"><font color="Green" title="E90">Lm34</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:132"/><span class="lab"><font color="Green" title="E110">A1</font></span>: 
<font color="Maroon" title="c4">F1</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="c5">F2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">F1</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="c5">F2</font></span><br/>

<span class="kw">then </span><span class="lab"><font color="Green" title="E111">A2</font></span>: <font color="Maroon" title="c4">F1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E69"><span class="lab"><font color="Green" title="E58">Lm22</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">F1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">H</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T20" target="_self" title="GROUP_9:th.20">Th20</a></span>
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">F1</font> = <font color="Maroon" title="c4">F1</font> 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="c5">F2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:132"><span class="lab"><font color="Green" title="E110">A1</font></span></a></span>;<br/>
<a NAME="E5:132"/>
<font color="Maroon" title="c7">F1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c6">F</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="c6">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T41" target="_self" title="GROUP_9:th.41">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:132"/>
<font color="Maroon" title="c3">H</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">F1</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="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:132"><span class="lab"><font color="Green" title="E111">A2</font></span></a>, <a class="ref" href="group_9.html#T39" target="_self" title="GROUP_9:th.39">Th39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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