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

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">H2</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>set </b><font color="Maroon" title="c4">A</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>;<br/>
<a NAME="E1:117"/><i><font color="Green" title="E80">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="group_2.html#T130" target="_self" title="GROUP_2:th.130">Th130</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c5">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="group_2.html#E1:117"><i><font color="Green" title="E80">A1</font></i></a>, <a class="txt" href="group_2.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E4:117"/><i><font color="Green" title="E81">A2</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="group_2.html#E1:117"><i><font color="Green" title="E80">A1</font></i></a>, <a class="ref" href="group_2.html#T34" target="_self" title="GROUP_2:th.34">Th34</a></i>;<br/>
<div><i><font color="Green" title="E82">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">g1</font>, <font color="Maroon" title="c8">g2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:117_1"/><i><font color="Green" title="E83">A4</font></i>: 
<font color="Maroon" title="c7">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:117_1"/><i><font color="Green" title="E84">A5</font></i>: 
<font color="Maroon" title="c8">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 ;<br/><b>consider </b><font color="Maroon" title="c9">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:117_1"/><i><font color="Green" title="E85">A6</font></i>: 
<font color="Maroon" title="c7">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">g</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E5:117_1"/><i><font color="Green" title="E86">A7</font></i>: 
<font color="Maroon" title="c9">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E1:117_1"><i><font color="Green" title="E83">A4</font></i></a>, <a class="ref" href="group_2.html#T34" target="_self" title="GROUP_2:th.34">Th34</a></i>;<br/><a NAME="E6:117_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T128" target="_self" title="GROUP_2:th.128">Th128</a></i>;<br/><b>then consider </b><font color="Maroon" title="c10">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E8:117_1"/><i><font color="Green" title="E87">A8</font></i>: 
<font color="Maroon" title="c8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">b</font>
 <b>and </b><br/><a NAME="E9:117_1"/><i><font color="Green" title="E88">A9</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">H2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="group_2.html#E2:117_1"><i><font color="Green" title="E84">A5</font></i></a>, <a class="ref" href="group_2.html#T33" target="_self" title="GROUP_2:th.33">Th33</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E11:117_1"/><i><font color="Green" title="E89">A10</font></i>: 
<font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font>
 <b>and </b><br/><a NAME="E12:117_1"/><i><font color="Green" title="E90">A11</font></i>: 
<font color="Maroon" title="c11">h</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E5:117_1"><i><font color="Green" title="E86">A7</font></i></a>, <a class="ref" href="group_2.html#T125" target="_self" title="GROUP_2:th.125">Th125</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E14:117_1"/><i><font color="Green" title="E91">A12</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E15:117_1"/><i><font color="Green" title="E92">A13</font></i>: 
<font color="Maroon" title="c12">c</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E9:117_1"><i><font color="Green" title="E88">A9</font></i></a>, <a class="ref" href="group_2.html#T126" target="_self" title="GROUP_2:th.126">Th126</a></i>;<br/><i><font color="Green" title="E93">A14</font></i>: <font color="Maroon" title="c7">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c8">g2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="group_2.html#E4:117_1"><i><font color="Green" title="E85">A6</font></i></a>, <a class="txt" href="group_2.html#E8:117_1"><i><font color="Green" title="E87">A8</font></i></a>, <a class="txt" href="group_2.html#E11:117_1"><i><font color="Green" title="E89">A10</font></i></a>, <a class="txt" href="group_2.html#E14:117_1"><i><font color="Green" title="E91">A12</font></i></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">c</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">c</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">c</font></span>)</span></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
;<br/><a NAME="E17:117_1"/>
<font color="Maroon" title="c11">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">c</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E12:117_1"><i><font color="Green" title="E90">A11</font></i></a>, <a class="txt" href="group_2.html#E15:117_1"><i><font color="Green" title="E92">A13</font></i></a>, <a class="ref" href="group_2.html#T59" target="_self" title="GROUP_2:th.59">Th59</a></i>;<br/><a NAME="E18:117_1"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">h</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">c</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="ref" href="group_2.html#T125" target="_self" title="GROUP_2:th.125">Th125</a></i>;<br/><b>hence </b><a NAME="E19:117_1"/>
<font color="Maroon" title="c7">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c8">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="group_2.html#E16:117_1"><i><font color="Green" title="E93">A14</font></i></a>, <a class="ref" href="group_2.html#T34" target="_self" title="GROUP_2:th.34">Th34</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E1:117_2"/>
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c8">g1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:117_2"/><i><font color="Green" title="E83">A15</font></i>: 
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>and </b><br/><a NAME="E4:117_2"/><i><font color="Green" title="E84">A16</font></i>: 
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="ref" href="group_2.html#T34" target="_self" title="GROUP_2:th.34">Th34</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">g2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E6:117_2"/><i><font color="Green" title="E85">A17</font></i>: 
<font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">g2</font>
 <b>and </b><br/><a NAME="E7:117_2"/><i><font color="Green" title="E86">A18</font></i>: 
<font color="Maroon" title="c9">g2</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E4:117_2"><i><font color="Green" title="E84">A16</font></i></a>, <a class="ref" href="group_2.html#T125" target="_self" title="GROUP_2:th.125">Th125</a></i>;<br/><i><font color="Green" title="E87">A19</font></i>: <font color="Maroon" title="c7">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="group_2.html#E3:117_2"><i><font color="Green" title="E83">A15</font></i></a>, <a class="txt" href="group_2.html#E6:117_2"><i><font color="Green" title="E85">A17</font></i></a>, <a class="ref" href="group_1.html#T25" title="GROUP_1:th.25">GROUP_1:25</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">g2</font></span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T19" title="GROUP_1:th.19">GROUP_1:19</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">g2</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T25" title="GROUP_1:th.25">GROUP_1:25</a></i>
;<br/><a NAME="E9:117_2"/>
<font color="Maroon" title="c9">g2</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E7:117_2"><i><font color="Green" title="E86">A18</font></i></a>, <a class="ref" href="group_2.html#T60" target="_self" title="GROUP_2:th.60">Th60</a></i>;<br/><a NAME="E10:117_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">g2</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">H2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T126" target="_self" title="GROUP_2:th.126">Th126</a></i>;<br/><a NAME="E11:117_2"/><b>then </b>
<font color="Maroon" title="c7">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="group_2.html#E8:117_2"><i><font color="Green" title="E87">A19</font></i></a>, <a class="ref" href="group_2.html#T33" target="_self" title="GROUP_2:th.33">Th33</a></i>;<br/><b>hence </b><a NAME="E12:117_2"/>
<font color="Maroon" title="c7">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T128" target="_self" title="GROUP_2:th.128">Th128</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:117"/>
 ex <font color="Olive" title="b1">H1</font> being <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="group_2.html#E4:117"><i><font color="Green" title="E81">A2</font></i></a>, <a class="txt" href="group_2.html#E5:117"><i><font color="Green" title="E82">A3</font></i></a>, <a class="ref" href="group_2.html#T61" target="_self" title="GROUP_2:th.61">Th61</a></i>;<br/>


</div>
