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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">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/><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">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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>





<b>assume </b><a NAME="E1:137"/><i><font color="Green" title="E113">A1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>then </b><i><font color="Green" title="E114">A2</font></i>: <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>
<b>by </b><i><a class="txt" href="group_9.html#E72"><i><font color="Green" title="E61">Lm22</font></i></a></i>
<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>
<b>by </b><i><a class="ref" href="group_9.html#T20" target="_self" title="GROUP_9:th.20">Th20</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c6">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> <b>by </b><i><a class="txt" href="group_9.html#E1:137"><i><font color="Green" title="E113">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">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> <b>by </b><i><a class="txt" href="group_9.html#E104"><i><font color="Green" title="E93">Lm34</font></i></a></i>;<br/>
<a NAME="E5:137"/>
<font color="Maroon" title="c6">F1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c7">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="c7">F</font>
 
<b>by </b><i><a class="ref" href="group_9.html#T41" target="_self" title="GROUP_9:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E6:137"/>
<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>
 <b>by </b><i><a class="txt" href="group_9.html#E2:137"><i><font color="Green" title="E114">A2</font></i></a>, <a class="ref" href="group_9.html#T39" target="_self" title="GROUP_9:th.39">Th39</a></i>; <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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