<?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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">G</font> being  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st  ex <font color="Olive" title="b3">H</font> being  <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="Olive" title="b2">G</font> st <font color="Olive" title="b3">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/>( <font color="Olive" title="b1">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Olive" title="b2">G</font> iff for <font color="Olive" title="b3">H</font> being  <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="Olive" title="b2">G</font>  st <font color="Olive" title="b3">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Olive" title="b1">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">H</font> )</span><br/><span class="kw">let </span><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>; <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">G</font> being  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st  ex <font color="Olive" title="b2">H</font> being  <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="Olive" title="b1">G</font> st <font color="Olive" title="b2">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/>( <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Olive" title="b1">G</font> iff for <font color="Olive" title="b2">H</font> being  <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="Olive" title="b1">G</font>  st <font color="Olive" title="b2">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">H</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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"> (  ex <font color="Olive" title="b1">H</font> being  <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="c3">G</font> st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  implies ( <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font> iff for <font color="Olive" title="b1">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font> ) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">X</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> ;<br/>
<span class="kw">assume </span><a NAME="E1:62"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 ex <font color="Olive" title="b1">H</font> being  <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="c3">G</font> st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font> iff for <font color="Olive" title="b1">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">H</font> being   <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="c3">G</font><span class="kw"> such that </span><br/><a NAME="E3:62"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<font color="Maroon" title="c5">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> 
 ;<br/>
<span class="kw">thus </span><a NAME="E4:62"/>
( <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font> implies for <font color="Olive" title="b1">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font> )
  <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">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font> ) implies <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:62_1"/>
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font>
 ; <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">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font></span><br/>

<a NAME="E2:62_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">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 <span class="p1">(<span class="default"><a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<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="E3:62_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A3</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="group_4.html#D8" target="_self" title="GROUP_4:def.8">Def8</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">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="c3">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  implies <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:62_1"/>
<font color="Maroon" title="c6">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">H</font></span><br/>

<a NAME="E5:62_1"/><span class="kw">then </span>
 <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <font color="Maroon" title="c6">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> 
 
;<br/>
<a NAME="E6:62_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">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">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62_1"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:62_1"/>
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">H</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>; <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><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E5:62"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
for <font color="Olive" title="b1">H</font> being  <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="c3">G</font>  st <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font></span><br/>

<div><span class="lab"><font color="Green" title="E33">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">Y</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span>  implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:62_2"/>
<font color="Maroon" title="c6">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font><span class="kw"> such that </span><br/><a NAME="E3:62_2"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c6">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font>
 <span class="kw">and </span><br/><a NAME="E4:62_2"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
 ex <font color="Olive" title="b1">H</font> being  <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="c3">G</font> st <br/>( <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">H</font> &amp; <font color="Olive" title="b1">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  )
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c8">H</font> being   <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="c3">G</font><span class="kw"> such that </span><br/><a NAME="E6:62_2"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">H</font>
 <span class="kw">and </span><br/><a NAME="E7:62_2"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c8">H</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:62_2"><span class="lab"><font color="Green" title="E35">A7</font></span></a></span>;<br/><a NAME="E8:62_2"/>
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c8">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:62"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E7:62_2"><span class="lab"><font color="Green" title="E37">A9</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E9:62_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62_2"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E6:62_2"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</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><span class="kw">end;</span></div>
<a NAME="E7:62"/>
 <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <font color="Maroon" title="c5">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E31">A2</font></span></a></span>;<br/>
<a NAME="E8:62"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">G</font> :  ex <font color="Olive" title="b2">K</font> being  <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="c3">G</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">K</font> &amp; <font color="Olive" title="b2">K</font> is  <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a>  ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:62"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/>
<a NAME="E9:62"/><span class="kw">then </span>
<font color="Maroon" title="c2">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 <span class="p1">(<span class="default"><a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="group_4.html#D8" target="_self" title="GROUP_4:def.8">Def8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:62"/>
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c3">G</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>; <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>
