<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span></span><br/>





<a NAME="E1:10"/>
( <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> &amp; <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grnilp_1.html#T9" target="_self" title="GRNILP_1:th.9">Th9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:10"/>
<span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <span class="p1"><a href="group_5.html#K8" title="GROUP_5:func.8">[.</a><span class="default"><font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><a href="group_5.html#K8" title="GROUP_5:func.8">.]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T64" title="GROUP_2:th.64">GROUP_2:64</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
