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

<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">N</font> being   <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">G</font><br/>  for <font color="Olive" title="b3">H1</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font> holds <br/> ( <font color="Olive" title="b3">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b2">N</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">H1</font> &amp; <font color="Olive" title="b2">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b3">H1</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">H1</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">N</font> being   <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="c2">G</font><br/>  for <font color="Olive" title="b2">H1</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> holds <br/> ( <font color="Olive" title="b2">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b1">N</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">H1</font> &amp; <font color="Olive" title="b1">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b2">H1</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">H1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   <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="c2">G</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">H1</font> being    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> holds <br/> ( <font color="Olive" title="b1">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">N</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">H1</font> &amp; <font color="Maroon" title="c3">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Olive" title="b1">H1</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">H1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">H1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">N</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="c4">H1</font> &amp; <font color="Maroon" title="c3">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H1</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="c4">H1</font> )</span><br/>







<span class="kw">thus </span><a NAME="E1:114"/>
<font color="Maroon" title="c4">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">N</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="c4">H1</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">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H1</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="c4">H1</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c5">A</font> = <font color="Maroon" title="c4">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">N</font> as    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c4">H1</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c6">N9</font> =  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">N</font> #) as   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E20"><span class="lab"><font color="Green" title="E19">Lm7</font></span></a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c7">H</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c4">H1</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="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c5">A</font> #) implies <font color="Maroon" title="c7">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  )</span><br/><span class="kw">assume </span><a NAME="E2:114_1_1"/><span class="lab"><font color="Green" title="E92">A1</font></span>: 
<font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c5">A</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="c7">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">H1</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="c8">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c8">b</font></span><br/><span class="kw">thus </span><a NAME="E1:114_1_1_1"/>
<font color="Maroon" title="c8">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c8">b</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="114_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c8">b</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:114_1_1_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c7">H</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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c8">b</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">H1</font><span class="kw"> such that </span><br/><a NAME="E3:114_1_1_1_1"/><span class="lab"><font color="Green" title="E93">A2</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">and </span><br/><a NAME="E4:114_1_1_1_1"/><span class="lab"><font color="Green" title="E94">A3</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T103" title="GROUP_2:th.103">GROUP_2:103</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">a9</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c12">b9</font> = <font color="Maroon" title="c8">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T2" target="_self" title="GROUP_9:th.2">Th2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">x9</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">H1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:114_1_1_1_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a></span>;<br/>
<a NAME="E7:114_1_1_1_1"/><span class="lab"><font color="Green" title="E95">A4</font></span>: 
<font color="Maroon" title="c12">b9</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T6" target="_self" title="GROUP_9:th.6">Th6</a></span>;<br/>
<a NAME="E8:114_1_1_1_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:114_1_1"><span class="lab"><font color="Green" title="E92">A1</font></span></a>, <a class="txt" href="#E4:114_1_1_1_1"><span class="lab"><font color="Green" title="E94">A3</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E9:114_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D25" target="_self" title="GROUP_9:def.25">Def28</a></span>;<br/>
<a NAME="E10:114_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <font color="Maroon" title="c6">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E11:114_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A5</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E12:114_1_1_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:114_1_1_1_1"><span class="lab"><font color="Green" title="E93">A2</font></span></a>, <a class="ref" href="group_9.html#T3" target="_self" title="GROUP_9:th.3">Th3</a></span>;<br/>
<a NAME="E13:114_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A6</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">b9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c6">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:114_1_1_1_1"><span class="lab"><font color="Green" title="E96">A5</font></span></a>, <a class="ref" href="group_2.html#T103" title="GROUP_2:th.103">GROUP_2:103</a></span>;<br/>
<a NAME="E14:114_1_1_1_1"/>
<font color="Maroon" title="c12">b9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c6">N9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">N9</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T118" title="GROUP_3:th.118">GROUP_3:118</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">b1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><span class="kw"> such that </span><br/><a NAME="E16:114_1_1_1_1"/><span class="lab"><font color="Green" title="E98">A7</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">b1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b9</font>
 <span class="kw">and </span><br/><a NAME="E17:114_1_1_1_1"/><span class="lab"><font color="Green" title="E99">A8</font></span>: 
<font color="Maroon" title="c14">b1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:114_1_1_1_1"><span class="lab"><font color="Green" title="E97">A6</font></span></a>, <a class="ref" href="group_2.html#T104" title="GROUP_2:th.104">GROUP_2:104</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">x99</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:114_1_1_1_1"><span class="lab"><font color="Green" title="E98">A7</font></span></a></span>;<br/>
<a NAME="E19:114_1_1_1_1"/>
<font color="Maroon" title="c14">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">x99</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b9</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:114_1_1_1_1"><span class="lab"><font color="Green" title="E98">A7</font></span></a>, <a class="ref" href="group_1.html#T14" title="GROUP_1:th.14">GROUP_1:14</a></span>;<br/>
<a NAME="E20:114_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A9</font></span>: 
<font color="Maroon" title="c14">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">x9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">b</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:114_1_1_1_1"><span class="lab"><font color="Green" title="E95">A4</font></span></a>, <a class="ref" href="group_9.html#T3" target="_self" title="GROUP_9:th.3">Th3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">b19</font> = <font color="Maroon" title="c14">b1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">H1</font> ;<br/>
<a NAME="E22:114_1_1_1_1"/>
<font color="Maroon" title="c14">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:114_1_1_1_1"><span class="lab"><font color="Green" title="E99">A8</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E23:114_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c4">H1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="group_9.html#K15" title="GROUP_9:func.15">carr</a> <font color="Maroon" title="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:114_1_1_1_1"><span class="lab"><font color="Green" title="E100">A9</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E24:114_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">b19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D25" target="_self" title="GROUP_9:def.25">Def28</a></span>;<br/>
<a NAME="E25:114_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A10</font></span>: 
<font color="Maroon" title="c16">b19</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c7">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:114_1_1"><span class="lab"><font color="Green" title="E92">A1</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E26:114_1_1_1_1"/>
<font color="Maroon" title="c16">b19</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:114_1_1_1_1"><span class="lab"><font color="Green" title="E98">A7</font></span></a>, <a class="ref" href="group_9.html#T3" target="_self" title="GROUP_9:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:114_1_1_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">H</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:114_1_1_1_1"><span class="lab"><font color="Green" title="E101">A10</font></span></a>, <a class="ref" href="group_2.html#T104" title="GROUP_2:th.104">GROUP_2:104</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/>


</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:114_1_1"/>
<font color="Maroon" title="c7">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T118" title="GROUP_3:th.118">GROUP_3:118</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:114_1"/>
<font color="Maroon" title="c4">H1</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c3">N</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="c4">H1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D10" target="_self" title="GROUP_9:def.10">Def10</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/>


</div><span class="kw">end;</span></div>

<span class="kw">hence </span><a NAME="E2:114"/>
<font color="Maroon" title="c3">N</font> <a href="group_9.html#K17" title="GROUP_9:func.17">/\</a> <font color="Maroon" title="c4">H1</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="c4">H1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
