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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>] means <font color="Maroon">a<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:48_1_1_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] or for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> holds not <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:48_1_1_1_1_1"/><i><font color="Green">E31</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/><div class="add"><a NAME="E2:48_1_1_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) </span>}</span> 
 <b>from </b><i><a class="ref" href="group_4.html#S1" target="_self">GROUP_4:sch 1</a>(<a class="txt" href="group_4.html#E1:48_1_1_1_1_1"><i><font color="Green">E31</font></i></a>);<br/></i><b>hence </b><a NAME="E3:48_1_1_1_1_1"/>
( ( ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) </span>}</span>  ) &amp; ( ( for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> holds not <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) ) )
 <b>by </b><i><a class="txt" href="group_4.html#E1:48_1_1_1_1_1"><i><font color="Green">E31</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:48_1_1_1_1_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> holds not <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a>
 ;<br/><div class="add"><a NAME="E2:48_1_1_1_1_2"/>
(  <a href="group_2.html#K6">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="group_2.html#K6">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><b>hence </b><a NAME="E3:48_1_1_1_1_2"/>
( ( ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) </span>}</span>  ) &amp; ( ( for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> holds not <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) ) )
 <b>by </b><i><a class="txt" href="group_4.html#E1:48_1_1_1_1_2"><i><font color="Green">E31</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:48_1_1"/>
( ( ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) </span>}</span>  ) &amp; ( ( for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> holds not <font color="Olive">b<sub>1</sub></font> is <a href="group_4.html#V2" target="_self">maximal</a> ) implies ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) ) )
 ;<br/>


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