<?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#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c2">A</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>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E35">A2</font></i>: 
for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b2">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green" title="E36">A3</font></i>: 
for <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">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>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c3">D</font> = <font color="Maroon" title="c2">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="group_2.html#E1:49"><i><font color="Green" title="E34">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">o</font> = the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font>;<br/>
<a NAME="E5:49"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c2">A</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c2">A</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<a NAME="E6:49"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c2">A</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E7:49"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:49_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:49_1"/><i><font color="Green" title="E38">A5</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span>
 <b>and </b><br/><a NAME="E4:49_1"/><i><font color="Green" title="E39">A6</font></i>: 
<span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">y1</font>, <font color="Maroon" title="c8">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:49_1"/><i><font color="Green" title="E40">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">y1</font>,<font color="Maroon" title="c8">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font>
 <b>by </b><i><a class="txt" href="group_2.html#E6:49"><i><font color="Green" title="E37">A4</font></i></a>, <a class="txt" href="group_2.html#E3:49_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T102" title="ZFMISC_1:th.102">ZFMISC_1:102</a></i>;<br/>
<a NAME="E7:49_1"/><i><font color="Green" title="E41">A8</font></i>: 
( <font color="Maroon" title="c7">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="txt" href="group_2.html#E6:49"><i><font color="Green" title="E37">A4</font></i></a>, <a class="txt" href="group_2.html#E3:49_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="group_2.html#E6:49_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">y1</font> = <font color="Maroon" title="c7">y1</font>, <font color="Maroon" title="c10">y2</font> = <font color="Maroon" title="c8">y2</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#E6:49"><i><font color="Green" title="E37">A4</font></i></a>, <a class="txt" href="group_2.html#E3:49_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="group_2.html#E6:49_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E9:49_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">y2</font>
 
<b>by </b><i><a class="txt" href="group_2.html#E3:49_1"><i><font color="Green" title="E38">A5</font></i></a>, <a class="txt" href="group_2.html#E4:49_1"><i><font color="Green" title="E39">A6</font></i></a>, <a class="txt" href="group_2.html#E6:49_1"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<b>hence </b><a NAME="E10:49_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="group_2.html#E2:49"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="group_2.html#E7:49_1"><i><font color="Green" title="E41">A8</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c5">o</font> = the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c3">D</font> <b>by </b><i><a class="txt" href="group_2.html#E6:49"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">H</font> =  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #);<br/>
<div><i><font color="Green" title="E38">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><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>let </b><font color="Maroon" title="c9">h1</font>, <font color="Maroon" title="c10">h2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #);<br/><b>assume </b><a NAME="E1:49_2"/><i><font color="Green" title="E39">A10</font></i>: 
( <font color="Maroon" title="c7">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h1</font> &amp; <font color="Maroon" title="c8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">h2</font> )
 ;<br/><a NAME="E2:49_2"/><i><font color="Green" title="E40">A11</font></i>: 
<font color="Maroon" title="c9">h1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">h1</font>,<font color="Maroon" title="c10">h2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><b>thus </b><a NAME="E3:49_2"/>
<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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">h2</font>
 <b>by </b><i><a class="txt" href="group_2.html#E1:49_2"><i><font color="Green" title="E39">A10</font></i></a>, <a class="txt" href="group_2.html#E2:49_2"><i><font color="Green" title="E40">A11</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div>
<a NAME="E10:49"/>
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #) is <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_3"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c7">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #);<br/>
<b>reconsider </b><font color="Maroon" title="c8">x</font> = <font color="Maroon" title="c7">a</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"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E3:49_3"/>
<font color="Maroon" title="c8">x</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>
 
<b>by </b><i><a class="txt" href="group_2.html#E3:49"><i><font color="Green" title="E36">A3</font></i></a></i>;<br/>
<a NAME="E4:49_3"/><b>then </b>
<font color="Maroon" title="c8">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</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="c2">A</font>
 
<b>by </b><i><a class="txt" href="group_2.html#E2:49"><i><font color="Green" title="E35">A2</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">t</font> =  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">G</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #) <b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">t</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D3" title="GROUP_1:def.3">GROUP_1:def 3</a><br/>

<b>let </b><font color="Maroon" title="c10">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #);<br/>

<b>reconsider </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c10">a</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"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon" title="c10">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">t</font> = 
<font color="Maroon" title="c11">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<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>
<b>by </b><i><a class="txt" href="group_2.html#E9:49"><i><font color="Green" title="E38">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c9">t</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">a</font> = 
<span class="p1">(<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> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="group_2.html#E9:49"><i><font color="Green" title="E38">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></i>
;<br/>

<b>reconsider </b><font color="Maroon" title="c12">s</font> = <font color="Maroon" title="c11">x</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #) <b>by </b><i><a class="txt" href="group_2.html#E3:49"><i><font color="Green" title="E36">A3</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c12">s</font>
;<br/>

<b>thus </b><font color="Maroon" title="c10">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">s</font> = 
<font color="Maroon" title="c11">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">x</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#E9:49"><i><font color="Green" title="E38">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">t</font>
<b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c12">s</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c10">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">x</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="c11">x</font>
<b>by </b><i><a class="txt" href="group_2.html#E9:49"><i><font color="Green" title="E38">A9</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">t</font>
<b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>
;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c7">H</font> =  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c5">o</font> #) as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">H</font> = <font color="Maroon" title="c7">H</font> as  <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> <b>by </b><i><a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">H</font>
;<br/>

<b>thus </b><a NAME="E13:49"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 ;<br/>


</div>
